EXHIBIT 31.1

# CERTIFICATION
BY CHIEF EXECUTIVE OFFICER
PURSUANT TO RULE 13a-14(a) and 15d-14(a) UNDER THE EXCHANGE ACT

I, James R. Gibbs, Chairman of the Board, President and Chief Executive Officer of Frontier Oil Corporation certify that:

|1. | I have reviewed this annual report on Form 10-K of Frontier Oil Corporation;                                                                                                                                                                                                                                        
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|2. | Based on my knowledge, this 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 report;
|3. | Based on my knowledge, the financial statements, and other financial information included in this report, fairly
     present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for,
     the periods presented in this report;                   
|4. | The registrants other certifying officers 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
      registrant 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 registrant,
         including its consolidated subsidiaries, is made known to us by others within those entities,
         particularly during the period in which this report is being prepared;
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| | b)  Evaluated the effectiveness of the registrants disclosure controls and procedures and presented in
         this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the
         end of the period covered by this report based on such evaluation; and                                                                                                     
| | c)  Disclosed in this report any change in the registrants internal control over financial reporting
         that occurred during the registrants most recent fiscal quarter that has materially affected, or is
         reasonably likely to materially affect, the registrants internal control over financial reporting; and                                                                          

|5. | The registrants other certifying officers and I have disclosed, based on our most recent evaluation of
     internal control over financial reporting, to the registrant's auditors and the audit committee of the
     registrant's board of directors (or persons performing the equivalent function):
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| | 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 registrants ability to record,
         process, summarize and report financial information; and
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| | b)  Any fraud, whether or not material, that involves management or other employees who have a
         significant role in the registrants internal control over financial reporting.                                                                                                       

March 8, 2004

| | /s/  James R. Gibbs 

                                                                                        James R. Gibbs
                                                                                Chairman of the Board, President
                                                                                  and Chief Executive Officer
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