Corporate Presentation January 2019 Developing Precision Medicines for the Treatment of Cancer Exhibit 99.1

Forward-Looking Statements This presentation contains forward-looking statements. Such statements include, but are not limited to, statements regarding our research, preclinical and clinical development activities, plans and projected timelines for tipifarnib, KO-947 and KO-539, plans regarding regulatory filings, our expectations regarding the relative benefits of our product candidates versus competitive therapies, and our expectations regarding the therapeutic and commercial potential of our product candidates. The words “believe,” “may,” “will,” “estimate,” “promise,” “plan”, “continue,” “anticipate,” “intend,” “expect,” “potential” and similar expressions (including the negative thereof), are intended to identify forward-looking statements. Because such statements are subject to risks and uncertainties, actual results may differ materially from those expressed or implied by such forward-looking statements. Risks that contribute to the uncertain nature of the forward-looking statements include: our preclinical studies and clinical trials may not be successful; the U.S. Food and Drug Administration (FDA) may not agree with our interpretation of the data from clinical trials of our product candidates; we may decide, or the FDA may require us, to conduct additional clinical trials or to modify our ongoing clinical trials; we may experience delays in the commencement, enrollment, completion or analysis of clinical testing for our product candidates, or significant issues regarding the adequacy of our clinical trial designs or the execution of our clinical trials may arise, which could result in increased costs and delays, or limit our ability to obtain regulatory approval; our product candidates may not receive regulatory approval or be successfully commercialized; unexpected adverse side effects or inadequate therapeutic efficacy of our product candidates could delay or prevent regulatory approval or commercialization; and we may not be able to obtain additional financing. Additional risks and uncertainties may emerge from time to time, and it is not possible for Kura’s management to predict all risk factors and uncertainties. All forward-looking statements contained in this presentation speak only as of the date on which they were made. Other risks and uncertainties affecting us are described more fully in our filings with the Securities and Exchange Commission. We undertake no obligation to update such statements to reflect events that occur or circumstances that exist after the date on which they were made.

* Includes cash, cash equivalents and short-term investments Investment Highlights Targeted Oncology Advance pipeline of targeted drug candidates for selected solid tumors and hematologic malignancies Utilize precision medicine approaches; Fast-to-market potential Proprietary Pipeline Tipifarnib: Potent farnesyl transferase inhibitor; Registration-directed and multiple Phase 2 trials ongoing; Biomarker-guided development; Issued patents and potential for regulatory exclusivity KO-947: ERK inhibitor; Phase 1 dose-escalation trial ongoing KO-539: Inhibitor of menin-MLL interaction; IND filing Q1 2019 Near-Term Milestones Additional Phase 2 data in HRAS mutant SCCs and CXCL12+ hematologic malignancies Team Proven oncology drug development experience Financials $187.4M cash as of September 30, 3018*

* Tipifarnib previously studied in > 5,000 patients in > 70 studies with a manageable safety profile as a single agent Note: Chemical structures of KO-947 and KO-539 not published Advancing Pipeline of Targeted Drug Candidates Tipifarnib KO-947 KO-539 Therapeutic Target Farnesyl transferase ERK kinase Menin-MLL interaction Biomarker Strategies HRAS mutant solid tumors CXCL12-expressing hematologic malignancies and solid tumors MAPK-pathway dysregulated tumors 11q13 amplified solid tumors MLL-rearranged (MLL-r) leukemias NPM1 and DNMT3A mutant liquid tumors Development Status Registration-directed study and multiple Phase 2 trials ongoing* Two biomarkers identified with issued patents Ongoing Phase 1 dose-escalation trial IND anticipated Q1 2019

Biomarker Strategies May Unlock Clinical Activity and Commercial Value Targeted Therapy Analytical Technologies Selected Patient Population Potential Value Enrichment of clinical activity Higher probability of success Expedited development and regulatory path Strong commercial case (next-generation sequencing, expression profiling, etc.)

HRAS Mutant HNSCC HRAS Mutant Allele Frequency Clinical benefit observed in high frequency HRAS mutant population Multiple Clinical Proof-of-Concepts Reinforce Precision Medicine Approach CXCL12+ High CXCL12 Levels Clinical benefit observed in high CXCL12 AITL / PTCL population AITL/PTCL

Note: Given current focus in HRAS mutant and CXCL12 pathway indications, Phase 2 study in MDS has been deprioritized and is not currently enrolling new patients Investigator-Sponsored Trials | HRAS Mutant Urothelial Carcinomas, Samsung Medical Center | HRAS Mutant Lung Squamous Cell Carcinomas (LSCC), Spanish Lung Cancer Group Product Candidate Pipeline Acute Leukemias KO-539 Menin-MLL Inhibitor Solid Tumors KO-947 ERK Inhibitor Phase 1 Pivotal Pancreatic AITL / PTCL Other SCCs HNSCC Preclinical Tipifarnib Farnesyl Transferase Inhibitor HRAS Mutant Indications CXCL12 Pathway Indications Preclinical Program Phase 2 CMML / AML MAPK Pathway Tumors Acute Leukemia

01 Tipifarnib in HRAS Mutant Solid Tumors KO-539 (Menin-MLL Inhibitor) 04 02 03 KO-947 (ERK Inhibitor) Tipifarnib Using CXCL12 Pathway Biomarkers

Tipifarnib is a Potent Inhibitor of HRAS Mutant Tumors Tumor Volume (mm3) Cetuximab 1mg Q4D Tipifarnib 80mg/kg BID Vehicle (Tipifarnib) Vehicle (Cetuximab) LU1513 HRAS Q61K (LSCC Model) Tipifarnib 80mg/kg BID Methotrexate 10mg/kg BIW Cetuximab 1mg QW Vehicle HN2606 HRAS G13R (HNSCC Model) Tumor Volume (mm3) Regressions observed in preclinical PDX models of SCC carrying the HRAS mutant oncogene Stasis or regression observed in other tumor types carrying HRAS mutations Treatment Days Treatment Days

Ho et al. European Society for Medical Oncology 2018 Congress #1046O | Preliminary results as of 9/7/18 * Response confirmed on 10/15/18 Phase 2 Study of Tipifarnib: HNSCC Patients (n=17 on study + 1 patient treated off protocol) Partial Response (n=6, +1 uPR off protocol) Stable Disease (n=4) Progressive Disease (n=1) Non Evaluable (adverse event [n=3] or w/o consent [n=2]) Pending 1st Response Assessment (n=1) 1 additional HNSCC patient treated off protocol with a 40% tumor size reduction at Cycle 2 (*)

Ho et al. European Society for Medical Oncology 2018 Congress #1046O | Preliminary results as of 9/7/18 Phase 2 Study of Tipifarnib: Other SCC Patients (n=6) Partial Response (n=1) Stable Disease (n=1) Progressive Disease Non Evaluable (n=2) Pending 1st Response Assessment (n=2) Baseline tumor HRAS G12S = 83% Plasma HRAS G12S (%) C1D1=18% C2D1=3% C2D22=0.3% Days

SD Non Evaluable PD Pending 1st Response Assessment 100 90 80 70 60 50 40 30 20 10 0 HRAS mutant AF (%, NGS) Ho et al. European Society for Medical Oncology 2018 Congress #1046 | Study KO-TIP-001 patients with HN and non-HN SCC tumors with available HRAS mutant allele data (10/17/18); one additional HNSCC patient was treated off protocol | * Allele frequency obtained post-ESMO | Pending analysis: 1 HNSCC pending 1st scan, 1 SCC pending 1st scan, 1 SCC SD n.d. A59T A59T G12S Q61L G13R G13S Q22K A18V Q61K G12S G12S* G13R G13R G12S G13V Q61K G12D G12S G12S G12S >20% HRAS mutant AF: 8 PR/uPR in 14 HNSCC/SCC patients (>20% AF ~5% HNSCC) >35% HRAS mutant AF: 6 PR/uPR in 8 patients PR or, uPR and ongoing (1) (1) (2) (4) (3) (1) (1) (4) (1) Non-HN SCC (2) d/c Cycle 2 (3) SD Cycle 4 ongoing (4) SD>6mo Association of HRAS Mutant Allele Frequency with Clinical Benefit from Tipifarnib (HNSCC, SCC, n=21)

RUN-HN KO-TIP-001 Phase 2 Proof-of-Concept Study SEQ-HN KO-TIP-007 Non-Interventional Screening & Outcomes Cohort AIM-HN KO-TIP-007 Registration-Directed Trial HRAS mutant patients who are not eligible for participation in AIM-HN may be referred to RUN-HN AIM-HN: Global, multi-center registration directed trial of tipifarnib in HRAS mutant HNSCC SEQ-HN: Matched control study to identify HRAS mutant HNSCC patients and characterize activity of standard of care Tipifarnib Development Program in HRAS Mutant HNSCC

Global, registration-directed trial Targeting ~ 100 clinical sites worldwide Anticipate ~ two years to enroll Primary endpoint: ORR by IRR Statistical assumptions At least 59 subjects, 80% power, 15% ORR (null hypothesis) and 30% ORR (response rate of interest) Minimum tumor HRAS mutant allele frequency of 20% Tumor HRAS mutation with an allele frequency ≥ 35%, or ≥ 20% if serum albumin is ≥ 3.5 g/dL 600 mg BID starting dose given daily in alternate weeks As currently designed, AIM-HN may be adequate to support an NDA seeking accelerated approval (FDA end of Phase 2 meeting) SEQ-HN data to provide a benchmark of the activity of standard of care in HRAS mutant HNSCC (relevant for potential label discussion and post approval commitments) Trial initiated and open for enrollment in November 2018 AIM-HN: Trial Design AIM-HN KO-TIP-007

Ho et al. European Society for Medical Oncology 2018 Congress #1046 | Study KO-TIP-001 patients with HN and non-HN SCC tumors with available HRAS mutant allele data (10/17/18); one additional HNSCC patient was treated off protocol | * Allele frequency obtained post-ESMO | Pending analysis: 1 HNSCC pending 1st scan, 1 SCC pending 1st scan, 1 SCC SD Activity When AIM-HN Criteria Applied Retrospectively to Phase 2 Study (HNSCC, SCC, n=21) 100 90 80 70 60 50 40 30 20 10 0 HRAS mutant AF (%, NGS) n.d. A59T A59T G12S Q61L G13R G13S Q22K A18V Q61K G12S G12S* G13R G13R G12S G13V Q61K G12D G12S G12S G12S ≥ 35% HRAS mutant AF, or ≥ 20% if serum albumin is ≥ 3.5 g/dL: 8 PR/uPR, 3 SD in 12 HNSCC/SCC patients SD Non Evaluable PD Pending 1st Response Assessment PR or, uPR and ongoing Patients who would have been excluded for low serum albumin Excluded Patients Included Patients

2,900-4,700 patients* HRAS Mutant HNSCC 1L 2L HNSCC Represents Significant Unmet Need1 Populations Based on Annual U.S. Incidence ORR 36% PFS 5.6 months OS ~10 months ORR 13-16% PFS ~2 months OS 6-8 months 1N Engl J Med. 2008 Sep 11;359(11):1116-27 | Keytruda & Opdivo package inserts | J Clin Oncol. 2007 Jun 1;25(16):2171-7 2 Journal of Clinical Oncology 2012 30:15_suppl, 5574-5574 * Estimate is between 5-8% of total HNSCC population, depending on allele frequency of HRAS mutations (Source: TCGA, internal data) HRAS Mutant Cancers: Market Opportunity 7,500+ patients HRAS Mutant All SCCs Outcome of SOC in unselected populations Lower response rate expected in HRAS mutant patients2

KO-539 (Menin-MLL Inhibitor) 04 02 01 03 KO-947 (ERK Inhibitor) Tipifarnib Using CXCL12 Pathway Biomarkers Tipifarnib in HRAS Mutant Solid Tumors

1 Burger et al. 2007. Br J Haematol. 137:288-96 | 2 Epstein 2004. Nat Rev Cancer 4:901-9 | 3 Feig et al. 2013. Proc Natl Acad Sci U S A. 110:20212-7 Key characteristics of CXCL12 Expressed primarily by immune cells, endothelial cells and stromal fibroblasts that constitute the tumor microenvironment Binds and activates two receptors, CXCR4 and CXCR7 CXCL12 and its receptors are key factors linking cancer cells with tumor microenvironment Potential role of CXCL12 inhibition in cancer therapy Inhibition of growth and homing of lymphoid and myeloid tumors1 Interference with tumor cell metastasis into secondary organs, e.g. inhibition of bone recurrence of solid tumors in adjuvant settings – after primary tumor is removed by surgery/chemoradiation2 Reversion of the tolerogenic effect of a tumor microenvironment rich in immunosuppressive cells such as regulatory T-cells and neutrophils, e.g. synergy of CXCL12 and PD-L1 inhibition in pancreatic tumor models3 Relevance of CXCL12 Inhibition as a Targeted Therapy

Primary CD1 mouse model of bone marrow cultures secrete abundant CXCL12 (SDF1, stroma derived factor 1) that was decreased by tipifarnib Research on specific farnesylated targets ongoing Witzig et al. ASH 2018 #2937; Kura Oncology Tipifarnib is a Potent Inhibitor of CXCL12 Secretion by Stromal Cells

KO-539 (Menin-MLL Inhibitor) 04 02a 01 03 KO-947 (ERK Inhibitor) Tipifarnib Using CXCL12 Pathway Biomarkers: PTCL / AITL Tipifarnib in HRAS Mutant Solid Tumors

1 Beleodaq® package insert 2 Istodax® package insert 3 Folotyn® package insert 4 1,000 mg/m2 administered over 30 mins by IV infusion once daily on days 1-5 of a 21-day cycle  5 14 mg/m2 administered over a 4-hour period by IV on days 1, 8 and 15 of a 28-day cycle  6 30 mg/m2 administered over 3-5 mins as an IV push once weekly for 6 weeks in 7-week cycles  PTCL: CXCL12-Expressing Lymphoma with a Significant Unmet Need BELEODAQ® (BELINOSTAT) ISTODAX® (ROMIDEPSIN) FOLOTYN® (PRALATREXATE) Efficacy Study Single Arm1 N=120 Single Arm2 N=130 Single Arm3 N=109 Prior Therapies (range) 2 (1-8) 2 (1-8) 3 (1-12) Overall Response Rate 25.8% 26.2% 27% Median PFS/TTP 1.6 months 4.0 months 3.5 months Median Overall Survival 7.9 months 11.3 months 14.5 months Dosing IV infusion4 IV infusion5 IV push6 Approved therapies in relapsed / refractory PTCL approved based on single-arm clinical trials of 130 patients or fewer with response rates in the range of 25-27% and limited duration of clinical benefit in unselected populations

Witzig et al. ASH 2018 #2937 | Preliminary data as of 11/21/18 | Missing measurement data from 2 subjects with best response of PD SPD: Sum of the products of diameters Clinical Activity in Phase 2 Study of Tipifarnib Change in SPD (%) AITL CXCL12 High PTCL PD SD PR CR

The High CXCL12/CXCR4 subset of PTCL patients experienced 50% ORR and 90% clinical benefit with tipifarnib after a median of 3 prior therapies High CXCL12/CXCR4 expression ratio had 90% sensitivity and 93% specificity to identify PTCL patients likely to benefit from tipifarnib Witzig et al. ASH 2018 #2937 | Preliminary data as of 11/21/18 | Expression data generated using RNA-Seq Association of High CXCL12 with Clinical Benefit from Tipifarnib in AITL/PTCL CR/PR SD PD/NE 8.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 CXCL12/CXCR4 Expression Ratio NOS AITL NOS NOS NOS AITL AITL AITCL AITL NOS NOS NOS NOS AITL AITL NOS AITL AITL NOS NOS AITL AITL NOS AITL 9 CR/PR/SD in 10 AITL/PTCL patients

Witzig et al. ASH 2018 #2937 A trend for worse prognosis was observed in PTCL patients with high CXCL12/CXCR4 expression ratio when treated with standard of care therapy Increasing levels of CXCL12 resulted in significantly more negative prognosis for SOC (not shown) CXCL12 high subset of patients represents ~40% of PTCL Ratio of CXCL12 to CXCR4 Expression Standard of Care Treatment High CXCL12 Defines Poor Prognosis with Standard of Care Therapy in PTCL

KO-539 (Menin-MLL Inhibitor) 04 02b 01 03 KO-947 (ERK Inhibitor) Tipifarnib Using CXCL12 Pathway Biomarkers: Other Hematologic Malignancies Tipifarnib in HRAS Mutant Solid Tumors

1 Blood. 2008 Mar 1;111(5):2589-96 | Expression data generated using microarray | HI: Hematologic Improvement CXCL12/CXCR4 Expression Ratio 1.4 0.4 0.3 0.2 0.1 0 Association of High CXCL12 with Activity of Tipifarnib in Elderly Unfit AML CR HI/SD PD/NE 7 CRs in 11 elderly unfit AML patients with high CXCL12 CTEP20 study: Patient subset – available AML marrow samples with NRAS WT or unknown, N=27 (NCBI GEO, GSE8970)1 Analysis limited to K/NRAS-wild type patients as K/NRAS mutant tumors are unlikely to be CXCL12-dependent

Witzig et al. Blood. 2011 Nov 3;118(18):4882-9 Opportunities in Other CXCL12-Expressing Hematologic Indications Responses previously observed in patients with other relapsed/refractory hematologic tumors (unselected population) in NCI-sponsored Phase 2 trial of tipifarnib Disease Type n CR, n (%) PR, n (%) ORR, (%) Diffuse large B-Cell Lymphoma (DLBCL) 37 0 7 (19) 19 Hodgkin Lymphoma 19 2 (11) 2 (11) 21 Mycosis Fungoides 4 0 2 (50) 50

KO-539 (Menin-MLL Inhibitor) 04 02c 01 03 KO-947 (ERK Inhibitor) Tipifarnib Using CXCL12 Pathway Biomarkers: Solid Tumors Tipifarnib in HRAS Mutant Solid Tumors

High CXCL12 expression consistently associated with reduced overall survival with standard of care in patients with pancreatic, esophagogastric and lung tumors1 1 Samarendra et al 2017. Br J Cancer 117, 124–135 Solid Tumors: Known Unmet Need in High CXCL12 Tumor Subsets

2019 ASCO Gastrointestinal Cancers Symposium January 18, 2019 | San Francisco, CA Poster Session B: Cancers of the Pancreas, Small Bowel and Hepatobiliary Tract Abstract 275: Patient reported abdominal pain as a surrogate of the clinical benefit of tipifarnib in pancreatic cancer patients Authors: Antonio Gualberto, Catherine Scholz, Eric Van Cutsem Demir et al. 2017. Early pancreatic cancer lesions suppress pain through CXCL12-mediated chemoattraction of Schwann cells. PNAS 114:E85-E94 Solid Tumors: Potential CXCL12-Driven Tumor Indication in Pancreatic Cancer

Cornerstone Proof-of-Concepts Support Expansion to Additional Indications Tipifarnib Farnesyl transferase (FT) inhibitor HRAS Mutant R/R HNSCC CXCL12+ R/R PTCL / AITL Other HRAS Mutant SCCs Earlier lines of therapy Other HRAS Mutant Solid Tumors Other CXCL12+ R/R B-cell Lymphomas Earlier lines of therapy CXCL12+ Solid Tumors (pancreatic) CXCL12+ AML / CMML CXCL12+ R/R CTCL, HL Earlier lines of therapy

U.S. patent 9,707,221 issued in July 2017 provides exclusivity for tipifarnib in HRAS mutant HNSCC indication to 2036 Corresponding patents beginning to issue in foreign countries U.S. patent 9,956,215 issued in May 2018 provides exclusivity for tipifarnib in certain CXCL12-expressing cancers to 2037 U.S. patent 10,137,121 issued in November 2018 provided exclusivity for tipifarnib in AITL to 2037 Additional patent applications pending in the U.S. and foreign countries for tipifarnib in other biomarkers and disease indications Patents illustrate potential of broader strategy to generate intellectual property related to use of drug candidates in biomarker-defined populations Biomarker Strategies Enlarge Patent Estate for Therapeutic Uses of Tipifarnib

KO-539 (Menin-MLL Inhibitor) 04 03 01 02 Tipifarnib Using CXCL12 Pathway Biomarkers Tipifarnib in HRAS Mutant Solid Tumors KO-947 (ERK Inhibitor)

Summary Potent, selective small molecule inhibitor of ERK1/2 Demonstrates prolonged pathway modulation in preclinical tumor models Multiple tumors, including SCCs and KRAS mutant adenocarcinomas, identified as sensitive to KO-947 as monotherapy in preclinical models Mechanism-based and SOC combinations under evaluation Clinical Development and Status Unique pharmacology enables intermittent dosing schedules Potential biomarkers, including 11q13 amplifications in SCCs, for sensitive subsets have been identified Phase 1 dose escalation trial ongoing Initial Phase 1 clinical data anticipated in 2019 KO-947: Potent Inhibitor of ERK1/2 KO-947 ERK inhibitor

Burrows et al. AACR 2017 #5168/11 KO-947 Demonstrates Robust Single-Agent Activity in Preclinical Studies

KO-947 (ERK Inhibitor) 03 04 01 02 Tipifarnib Using CXCL12 Pathway Biomarkers Tipifarnib in HRAS Mutant Solid Tumors KO-539 (Menin-MLL Inhibitor)

Summary Potent, selective small molecule inhibitor of the menin-MLL interaction Robust antitumor activity observed in mixed lineage leukemias rearranged (MLL-r) as well as disseminated NPM1mut and DNMT3Amut AML PDX models Preliminary data suggests anti-leukemic activity by induction of myeloid differentiation in AML blasts Menin-MLL inhibitors have the potential to treat approximately 50% of acute leukemias Status IND submission anticipated in Q1 2019 Initiation of Phase 1 study anticipated in Q2 2019 KO-539: Potent Inhibitor of Menin-MLL Interaction KO-539 Menin-MLL inhibitor The menin-MLL complex appears to be a central node in epigenetic dysregulation driven by several distinct oncogenic driver mutations important in diverse leukemias and myeloproliferative disorders

Last dose Vehicle KO-539 100 mg/kg QD Quizartinib 3 mg/kg QD Percent Survival Days of Therapy Burrows et al. AACR-NCI-EORTC 2017 LB-A27 CD45+ human AML blasts Overall survival Percent Circulating WBC Days of Therapy Tolerability Days of Therapy Bodyweight (g) KO-539 Produces Lasting Complete Remissions in a NPM1/DNMT3A/IDH2/FLT3-Mutant AML Model AM7577 Model

* As of 3Q 2018 10-Q Anticipated Milestones & Financial Highlights Tipifarnib Farnesyl Transferase Inhibitor HRAS Mutant Indications CXCL12 Pathway Indications KO-539 Menin-MLL Inhibitor KO-947 ERK Inhibitor Phase 1 Status Milestones Program Initiation of registration-directed trial in HNSCC ü Additional data from Phase 2 trial (KO-TIP-001) 2019 Patents for tipifarnib in AITL and CXCL12+ PTCL & AML ü Proof-of-concept in AITL ü Data from retrospective study in pancreatic cancer Q1 2019 Data update in CXCL12+ hematologic malignancies 2019 Potential biomarker of activity in squamous cell carcinomas ü Data from Phase 1 dose-escalation trial 2019 Anti-tumor activity in preclinical models of AML ü Submission of IND application Q1 2019 Initiation of Phase 1 trial Q2 2019 $187.4M Financial Highlights Nasdaq: KURA Shares outstanding: 38.0M basic, 3.3M options* Cash, cash equivalents and short-term investments: $187.4M*

Corporate Presentation January 2019 Developing Precision Medicines for the Treatment of Cancer