Exhibit 5.1

McGuireWoods LLP

One James Center

Richmond, Virginia 23219

July 3, 2014

Board of Directors

Dominion Gas Holdings, LLC

120 Tredegar Street

Richmond, Virginia 23219

Dominion Gas Holdings, LLC

Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as special counsel to Dominion Gas Holdings, LLC, a Virginia limited liability company (the “Company”), in connection with the Registration Statement on Form S-3 (the “Registration Statement”) being filed by the Company on or about the date of this opinion letter with the Securities and Exchange Commission (the “SEC”) in connection with the registration under the Securities Act of 1933, as amended (the “Securities Act”), of certain Senior Debt Securities and Junior Subordinated Notes (the Senior Debt Securities and Junior Subordinated Notes, collectively, the “Debt Securities”). This opinion letter is being furnished in accordance with the requirements of Item 16 of Form S-3 and Item 601(b)(5)(i) of Regulation S-K promulgated under the Securities Act. Capitalized terms used and not defined herein shall have the meanings assigned to them in the Registration Statement or the Indentures (as defined below).

The Debt Securities are described in the Registration Statement. We understand that the Debt Securities will be issued pursuant to: (i) that certain Senior Indenture dated as of October 1, 2013, between the Company and Deutsche Bank Trust Company Americas, as trustee, as heretofore supplemented (as so supplemented, the “Senior Indenture”) and as further supplemented from time to time by supplemental indentures (the “Senior Supplemental Indentures”), each to be entered into by the Company and such trustee or (ii) a Subordinated Note Indenture (the “Subordinated Indenture,” and together with the Senior Indenture, collectively, the “Base Indentures”), to be entered into at a future date between the Company and Deutsche Bank Trust Company Americas, as trustee, as supplemented from time to time by supplemental indentures (the “Subordinated Note Supplemental Indentures,” and together with the Senior Supplemental Indentures, collectively, the “Supplemental Indentures”; and each Base Indenture, as supplemented by the applicable Supplemental Indenture, an “Indenture,” and collectively, the “Indentures”), each to be entered into between the Company and such trustee.

Documents Reviewed

In connection with this opinion letter, we have examined the following documents:

(a) the Registration Statement, including the exhibits being filed therewith and incorporated by reference therein from previous filings made by the Company with the SEC (which exhibits include the Indentures) and

(b) the prospectus contained in the Registration Statement (the “Prospectus”).

In addition we have examined and relied upon the following:

(i) a certificate from the assistant secretary of the Company certifying as to (A) true and correct copies of the articles of organization and operating agreement of the Company (the “Organizational Documents”) and (B) the resolutions of the Board of the Company authorizing the filing of the Registration Statement and the issuance of the Debt Securities by the Company subject to (1) in the case of each issuance of Debt Securities, a specific further authorization for the issuance, execution, delivery and performance by proper action of the Company’s Board, an authorized committee or authorized officers (the “Authorizing Resolutions”) with respect to such Debt Securities and (2) the other qualifications set forth therein;

(ii) a certificate dated July 3, 2014 issued by the State Corporation Commission of the Commonwealth of Virginia (the “SCC”), attesting to the limited liability company status of the Company in the Commonwealth of Virginia (the “Status Certificate”); and

(iii) originals, or copies identified to our satisfaction as being true copies, of such other records, documents and instruments as we have deemed necessary for the purposes of this opinion letter.

“Applicable Law” means the law of the Commonwealth of Virginia and the State of New York and the relevant laws of the United States.

Assumptions Underlying Our Opinions

For all purposes of the opinions expressed herein, we have assumed, without independent investigation, the following:

(a) Factual Matters. To the extent that we have reviewed and relied upon (i) certificates of the Company or authorized representatives thereof and (ii) certificates and assurances from public officials, all of such certificates, representations and assurances are accurate with regard to factual matters.

(b) Signatures. The signatures of individuals who have signed or will sign the Indentures are genuine and (other than those of individuals signing on behalf of the Company at or before the date hereof) authorized.

(c) Authentic and Conforming Documents. All documents submitted to us as originals are authentic, complete and accurate, and all documents submitted to us as copies conform to authentic original documents.

(d) Organizational Status, Power and Authority and Legal Capacity of Certain Parties. All parties to the Indentures are, or were at the time the Senior Indenture was executed and delivered, or will be validly existing and in good standing in their respective jurisdictions of formation and have, had at the time the Senior Indenture was executed and delivered, or will have the capacity and full power and authority to execute, deliver and perform the Indentures and the documents required or permitted to be delivered and performed thereunder, except that no such assumption is made as to the Company as of the date of the Status Certificate. All individuals who have signed or will sign each Indenture had or will have the legal capacity to execute such Indenture.

2

(e) Authorization, Execution and Delivery of Indentures. The Indentures and the documents required or permitted to be delivered thereunder have been or will be duly authorized by all necessary corporate, limited liability company, business trust, partnership or other action on the part of the parties thereto and have been or will be duly executed and delivered by such parties.

(f) Indentures Binding on Certain Parties. The Indentures and the documents required or permitted to be delivered thereunder are or will be valid and binding obligations enforceable against the parties thereto in accordance with their terms, except no such assumption is made as to the Company with respect to the Senior Indenture as of the date hereof.

(g) Governing Law of Certain Documents. Each Supplemental Indenture will be consistent with the form required by the applicable Base Indenture. Each Supplemental Indenture will be governed by the laws of the State of New York.

(h) Noncontravention. Neither the issuance of the Debt Securities by the Company or the execution and delivery of the Indentures by any party thereto nor the performance by such party of its obligations thereunder will conflict with or result in a breach of (i) the certificate or articles of incorporation, bylaws, certificate or articles of organization, operating agreement, certificate of limited partnership, partnership agreement, trust agreement or other similar organizational documents of any such party, (ii) any law or regulation of any jurisdiction applicable to any such party, or (iii) any order, writ, injunction or decree of any court or governmental instrumentality or agency applicable to any such party or any agreement or instrument to which any such party may be a party or by which its properties are subject or bound.

(i) Governmental Approvals. All consents, approvals and authorizations of, or filings with, all governmental authorities that are required as a condition to the issuance of the Debt Securities or to the execution and delivery of the Indentures by the parties thereto or the performance by such parties of their obligations thereunder will have been obtained or made.

(j) Registration; Trust Indenture Act. The Registration Statement will be effective under the Securities Act and the Indentures will be qualified under the Trust Indenture Act of 1939.

(k) No Mutual Mistake. There has not been, and will not be, any mutual mistake of fact, fraud, duress or undue influence in connection with the issuance of the Debt Securities as contemplated by the Registration Statement, Prospectus and any supplements to the Prospectus.

3

Our Opinions

Based on and subject to the foregoing and the exclusions, qualifications, limitations and other assumptions set forth in this opinion letter, we are of the opinion that:

1. Organizational Status. Based solely upon its Status Certificate, the Company is a validly existing limited liability company under the laws of the Commonwealth of Virginia.

2. Power and Authority. The Company has the limited liability company power and authority to issue the Debt Securities.

3. Debt Securities. With respect to any Debt Securities, when (i) Authorizing Resolutions with respect to such Debt Securities have been adopted, (ii) the terms of such Debt Securities and the terms for their issuance and sale have been established in conformity with such Authorizing Resolutions and the applicable Indenture, (iii) such Debt Securities have been issued and sold as contemplated by the Registration Statement, the Prospectus and the applicable supplement to such Prospectus, (iv) the Company has received the consideration provided for in the applicable supplement to the Prospectus and any applicable definitive purchase, underwriting or similar agreement and (v) such Debt Securities have been authenticated in accordance with the provisions of the applicable Indenture, such Debt Securities will constitute the valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

Matters Excluded from Our Opinions

We express no opinion with respect to the following matters:

(a) Indemnification and Change of Control. The enforceability of any agreement of the Company in an Indenture relating to (i) indemnification, contribution or exculpation from costs, expenses or other liabilities or (ii) changes in the organizational control or ownership of the Company, which agreement (in the case of clause (i) or clause (ii)) is contrary to public policy or applicable law.

(b) Jurisdiction, Venue, etc. The enforceability of any agreement of the Company in the Indentures to submit to the jurisdiction of any specific federal or state court (other than the enforceability in a court of the State of New York of any such agreement to submit to the jurisdiction of a court of the State of New York), to waive any objection to the laying of the venue, to waive the defense of forum non conveniens in any action or proceeding referred to therein, to waive trial by jury, to effect service of process in any particular manner or to establish evidentiary standards, and any agreement of the Company regarding the choice of law governing an Indenture (other than the enforceability in a court of the State of New York or in a federal court sitting in the State of New York and applying New York law to any such agreement that the laws of the State of New York shall govern an Indenture).

Qualifications and Limitations Applicable to Our Opinions

The opinions set forth above are subject to the following qualifications and limitations:

(a) Applicable Law. Our opinions are limited to the Applicable Law, and we do not express any opinion concerning any other law.

4

(b) Bankruptcy. Our opinions are subject to the effect of any applicable bankruptcy, insolvency (including, without limitation, laws relating to preferences, fraudulent transfers and equitable subordination), reorganization, moratorium and other similar laws affecting creditors’ rights generally.

(c) Equitable Principles. Our opinions are subject to the effect of general principles of equity (regardless of whether considered in a proceeding in equity or at law), including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing. In applying such principles, a court, among other things, might limit the availability of specific equitable remedies (such as injunctive relief and the remedy of specific performance), might not allow a creditor to accelerate maturity of debt or exercise other remedies upon the occurrence of a default deemed immaterial or for non-credit reasons or might decline to order a debtor to perform covenants in an Indenture.

(d) Choice of New York Law and Forum. To the extent that any opinion relates to the enforceability of the choice of New York law or any choice of New York forum provisions of any Indenture, our opinion is rendered in reliance upon N.Y. Gen. Oblig. Law §§ 5-1401 and 5-1402 and N.Y. CPLR 327(b) and is subject to the qualification that such enforceability may be limited by principles of public policy, comity and constitutionality. We express no opinion as to whether a United States federal court would have subject-matter or personal jurisdiction over a controversy arising under the Indentures.

(e) Currency Conversion. We advise you that a judgment for money relating to any obligation under a Debt Security or an Indenture denominated in a currency other than United States dollars ordinarily would be rendered or enforced only in United States dollars by a court of the State of New York or a United States court sitting in the State of New York and applying New York law. The method used to determine the rate of conversion of a foreign currency into United States dollars will depend on various factors.

Miscellaneous

The foregoing opinions are being furnished only for the purpose referred to in the first paragraph of this opinion letter. Our opinions are based on statutes, regulations and administrative and judicial interpretations which are subject to change. We undertake no responsibility to update or supplement these opinions subsequent to the effective date of the Registration Statement. We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement on or about the date hereof, to the incorporation by reference of this opinion of counsel into the Registration Statement and to the reference to our firm in the Prospectus under the caption “Legal Matters.” In giving this consent, we do not admit that we are within the category of persons whose consent is required by Section 7 of the Securities Act or the rules and regulations of the SEC promulgated thereunder.

Very truly yours,

/s/ McGuireWoods LLP

5