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                                                                    EXHIBIT 24.3
 
                               POWER OF ATTORNEY
 
KNOW ALL MEN BY THESE PRESENTS:
 
     WHEREAS, Chevron Corporation, a Delaware corporation (the "Corporation"),
contemplates filing with the Securities and Exchange Commission at Washington,
D.C., S-4 Registration Statement.
 
     WHEREAS, the undersigned is an officer or director of the Corporation.
 
     NOW, THEREFORE, the undersigned hereby constitutes and appoints LYDIA I.
BEEBE, HILMAN P. WALKER, TERRY MICHAEL KEE AND KEITH J. MENDELSON, or any of
them, his or her attorneys-in-fact and agents, with full power of substitution
and resubstitution, for such person and in his or her name, place and stead, in
any and all capacities, to sign the aforementioned document (and any and all
amendments thereto) and to file the same, with any exhibits thereto, and other
documents in connection therewith, with the Securities and Exchange Commission,
granting unto said attorneys-in-fact and agents full power and authority to do
and perform each and every act and thing requisite and necessary to be done in
and about the premises, as fully as to all intents and purposes he or she might
or could do in person, hereby ratifying and confirming all that said
attorneys-in-fact and agents, or their substitutes, may lawfully do and cause to
be done by virtue hereof.
 
     IN WITNESS WHEREOF, the undersigned has hereunto set his or her hand this
11th day of February, 1999.
 
                                                 /s/ DAVID J. O'REILLY
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