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                                                                    EXHIBIT 23.3
 
                          CONSENT OF FINANCIAL ADVISOR
 
     We consent to the use of our fairness opinion letter dated December 23,
1998 forming a part of this Registration Statement on Form S-4 filed by Chevron
Corporation in connection with the merger of Chevron Corporation and
Rutherford-Moran Oil Corporation, to be included in this proxy statement/
prospectus. We also consent to the references to our fairness opinion letter,
the analysis conducted by us and the use of our name in this proxy
statement/prospectus under the headings "Summary" and "The Merger."
 
Bear Stearns & Co., Inc.
February 11, 1999