Exhibit 31.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO SECTION 302

OF THE SARBANES-OXLEY ACT OF 2002

I, Burt Sugarman, certify that:

1. I have reviewed this quarterly report on Form 10-Q for the third quarterly period ended September 30, 2004 (“Quarterly Report”) of GIANT GROUP, LTD. (“Company” or “Registrant”);

2. Based on my knowledge, this Quarterly Report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this Quarterly Report;

3. Based on my knowledge, the financial statements and other financial information included in this Quarterly Report, fairly present in all material respects the financial condition, results of operations and cash flows of the Company as of, and for the periods presented in this Quarterly Report;

4. The Registrant’s other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures, as defined in Exchange Act rules 13a-15(e) and 15d-15(e) for the Company and have:

(a) Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the Company is made known to us during the period in which this Quarterly Report is being prepared;

(b) Evaluated the effectiveness of the Company’s disclosure controls and procedures and presented in this Quarterly Report our conclusions about the effectiveness of the disclosure controls and procedures, as of the period ended of September 30, 2004 covered by this Quarterly Report based on such evaluation; and

(c) Disclosed in this Quarterly Report any change in the Company’s internal control over financial reporting that occurred during the Company’s most recent fiscal quarter that has materially affected, or is reasonably likely to materially affect, the Company’s internal control over financial reporting; and

5. The Registrant’s other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the Company’s independent auditor and the Audit Committee of the Board of Directors:

(a) All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the Company’s ability to record, process, summarize and report financial information; and

(b) Any fraud, whether or not material, that involves management or other employees who have a significant role in the Company’s internal control over financial reporting.

Date: November 12, 2004

/s/    BURT SUGARMAN        

Chief Executive Officer