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 *
ROBERTSON PETER 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)
Vice Chairman of the Board
(Last)
(First)
(Middle)
6001 BOLLINGER CANYON ROAD		 3. Date of Earliest Transaction (Month/Day/Year)
05/28/2008
(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 05/28/2008   M   160,000 A $ 43.125 187,338 (1) D  
Common Stock 05/28/2008   S   96,449 D $ 99 90,889 D  
Common Stock 05/28/2008   S   3,600 D $ 99.005 87,289 D  
Common Stock 05/28/2008   S   23,055 D $ 99.01 64,234 D  
Common Stock 05/28/2008   S   3,800 D $ 99.015 60,434 D  
Common Stock 05/28/2008   S   12,088 D $ 99.02 48,346 D  
Common Stock 05/28/2008   S   300 D $ 99.025 48,046 D  
Common Stock 05/28/2008   S   2,700 D $ 99.03 45,346 D  
Common Stock 05/28/2008   S   2,677 D $ 99.035 42,669 D  
Common Stock 05/28/2008   S   800 D $ 99.04 41,869 D  
Common Stock 05/28/2008   S   1,800 D $ 99.045 40,069 D  
Common Stock 05/28/2008   S   7,220 D $ 99.05 32,849 D  
Common Stock 05/28/2008   S   600 D $ 99.055 32,249 D  
Common Stock 05/28/2008   S   645 D $ 99.06 31,604 D  
Common Stock 05/28/2008   S   2,900 D $ 99.065 28,704 D  
Common Stock 05/28/2008   S   100 D $ 99.07 28,604 D  
Common Stock 05/28/2008   S   1,266 D $ 99.08 27,338 D  
Common Stock               44,940 (2) I by 401(k) plan
Common Stock               7,100 I by Spouse GRAT
Common Stock               7,100 I by GRAT

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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
Non-Qualified Stock Option (Right to Buy) $ 43.125 (3) 05/28/2008   M     160,000 (3)   (4) 06/26/2012 Common Stock 160,000 (3) $ 0 0 D  

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
ROBERTSON PETER J
6001 BOLLINGER CANYON ROAD
SAN RAMON, CA 94583		   X     Vice Chairman of the Board  

Signatures

 Christopher A. Butner on behalf of Peter J. Robertson   05/29/2008
**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) This number includes dividend equivalent accruals (234 shares) from awards granted under the Chevron Long-Term Incentive Plan.
(2) Between December 6, 2007 and May 28, 2008, the reporting person acquired 800 shares of Chevron Corporation common stock under the Chevron Employee Savings Investment Plan, a 401(k) plan.
(3) The option exercise price and number of shares are adjusted for the September 10, 2004, 2-for-1 stock split of Chevron Corporation common stock.
(4) One-third of the shares subject to the option vested on each of the first, second and third anniversaries of the June 26, 2002 date of grant.

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