Ownership Submission
FORM 4
Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).
UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES

Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940
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(Print or Type Responses)
1. Name and Address of Reporting Person *
O REILLY DAVID J
   2. Issuer Name and Ticker or Trading Symbol
CHEVRON CORP [CVX] 		5. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
__X__ Director _____ 10% Owner
__X__ Officer (give title below) _____ Other (specify below)
Chairman of the Board and CEO
(Last)
(First)
(Middle)
6001 BOLLINGER CANYON ROAD		 3. Date of Earliest Transaction (Month/Day/Year)
05/07/2008
(Street)

SAN RAMON, CA 94583		 4. If Amendment, Date Original Filed(Month/Day/Year)
 6. Individual or Joint/Group Filing(Check Applicable Line)
_X_ Form filed by One Reporting Person
___ Form filed by More than One Reporting Person
(City)
(State)
(Zip)
Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security
(Instr. 3)		 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code
(Instr. 8)		 4. Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4 and 5)		 5. Amount of Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 3 and 4)		 6. Ownership Form: Direct (D) or Indirect (I)
(Instr. 4)		 7. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V Amount (A) or (D) Price
Common Stock 05/07/2008   S   1,406 (1) D $ 95.915 53,836 D  
Common Stock 05/07/2008   S   2,504 D $ 95.92 51,332 D  
Common Stock 05/07/2008   S   2,300 D $ 95.925 49,032 D  
Common Stock 05/07/2008   S   800 D $ 95.9275 48,232 D  
Common Stock 05/07/2008   S   1,201 D $ 95.93 47,031 D  
Common Stock 05/07/2008   S   800 D $ 95.935 46,231 D  
Common Stock 05/07/2008   S   100 D $ 95.9375 46,131 D  
Common Stock 05/07/2008   S   100 D $ 95.99 46,031 D  
Common Stock 05/07/2008   S   200 D $ 96 45,831 D  
Common Stock 05/07/2008   S   700 D $ 96.01 45,131 D  
Common Stock 05/07/2008   S   300 D $ 96.015 44,831 D  
Common Stock 05/07/2008   S   5,481 D $ 96.02 39,350 D  
Common Stock 05/07/2008   S   300 D $ 96.025 39,050 D  
Common Stock 05/07/2008   S   700 D $ 96.03 38,350 D  
Common Stock 05/07/2008   S   700 D $ 96.07 37,650 D  
Common Stock 05/07/2008   S   1,300 D $ 96.1 36,350 D  
Common Stock 05/07/2008   S   900 D $ 96.105 35,450 D  
Common Stock 05/07/2008   S   400 D $ 96.1075 35,050 D  
Common Stock 05/07/2008   S   1,100 D $ 96.11 33,950 D  
Common Stock 05/07/2008   S   200 D $ 96.115 33,750 D  
Common Stock 05/07/2008   S   300 D $ 96.12 33,450 D  
Common Stock 05/07/2008   S   1,300 D $ 96.125 32,150 D  
Common Stock 05/07/2008   S   300 D $ 96.1275 31,850 D  
Common Stock 05/07/2008   S   300 D $ 96.13 31,550 D  
Common Stock 05/07/2008   S   400 D $ 96.135 31,150 D  
Common Stock 05/07/2008   S   550 D $ 96.15 30,600 D  
Common Stock 05/07/2008   S   2,600 D $ 96.16 28,000 D  
Common Stock 05/07/2008   S   2,000 D $ 96.17 26,000 D  

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 3)		 2. Conversion or Exercise Price of Derivative Security 3. Transaction Date (Month/Day/Year) 3A. Deemed Execution Date, if any (Month/Day/Year) 4. Transaction Code
(Instr. 8)		 5. Number of Derivative Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4, and 5)		 6. Date Exercisable and Expiration Date
(Month/Day/Year)		 7. Title and Amount of Underlying Securities
(Instr. 3 and 4)		 8. Price of Derivative Security
(Instr. 5)		 9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 4)		 10. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 4)		 11. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V (A) (D) Date Exercisable Expiration Date Title Amount or Number of Shares

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
O REILLY DAVID J
6001 BOLLINGER CANYON ROAD
SAN RAMON, CA 94583		   X     Chairman of the Board and CEO  

Signatures

 Christopher A. Butner on behalf of David J. O'Reilly   05/08/2008
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 4(b)(v).
** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1) The Form 4 is five of six being filed to report transactions occurring on May 7, 2008.

Note: File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure.

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