Frontier Oil (FTO) 10-Q 2008 Q2 Quarterly report

Exhibit 32.1

CERTIFICATION BY CHIEF EXECUTIVE OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Frontier Oil Corporation (the “Company”) on Form 10-Q for the period ending June 30, 2008, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, James R. Gibbs, Chairman of the Board, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, to my knowledge, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ James R. Gibbs

James R. Gibbs

Chairman of the Board, President and

Chief Executive Officer

August 7, 2008