In connection with the Annual Report of Frontier Oil Corporation (the “Company”) on Form 10-K/A for the period ending December 31, 2003 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 result of operations of the Company. |
/s/ James R. Gibbs
James R. Gibbs
Chairman of the Board, President and
Chief Executive Officer
October 13, 2004
