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 *
HESS JOHN B
   2. Issuer Name and Ticker or Trading Symbol
HESS CORP [HES] 		5. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
__X__ Director __X__ 10% Owner
__X__ Officer (give title below) _____ Other (specify below)
Chairman of the Board and CEO
(Last)
(First)
(Middle)
HESS CORPORATION, 1185 AVENUE OF THE AMERICAS		 3. Date of Earliest Transaction (Month/Day/Year)
04/07/2008
(Street)

NEW YORK, NY 10036		 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, $1.00 par value 04/07/2008   S(1)   200 D $ 97.78 1,288,569 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 95.78 1,288,469 D  
Common Stock, $1.00 par value 04/07/2008   S   200 D $ 95.93 1,288,269 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 97.12 1,288,169 D  
Common Stock, $1.00 par value 04/07/2008   S   200 D $ 97.93 1,287,969 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 98.12 1,287,869 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 96.31 1,287,769 D  
Common Stock, $1.00 par value 04/07/2008   S   300 D $ 97.39 1,287,469 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 96.88 1,287,369 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 97.09 1,287,269 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 97.8 1,287,169 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 98.09 1,287,069 D  
Common Stock, $1.00 par value 04/07/2008   S   300 D $ 96.09 1,286,769 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 96.01 1,286,669 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 97.19 1,286,569 D  
Common Stock, $1.00 par value 04/07/2008   S   200 D $ 97.9 1,286,369 D  
Common Stock, $1.00 par value 04/07/2008   S   300 D $ 97.98 1,286,069 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 98.11 1,285,969 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 95.9 1,285,869 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 95.98 1,285,769 D  
Common Stock, $1.00 par value 04/07/2008   S   400 D $ 97.54 1,285,369 D  
Common Stock, $1.00 par value 04/07/2008   S   300 D $ 97.5 1,285,069 D  
Common Stock, $1.00 par value 04/07/2008   S   600 D $ 97.58 1,284,469 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 97.45 1,284,369 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 96.45 1,284,269 D  
Common Stock, $1.00 par value 04/07/2008   S   200 D $ 97.32 1,284,069 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 96.32 1,283,969 D  
Common Stock, $1.00 par value 04/07/2008   S   500 D $ 97.55 1,283,469 D  
Common Stock, $1.00 par value 04/07/2008   S   100 D $ 96.55 1,283,369 (2) D  

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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
HESS JOHN B
HESS CORPORATION
1185 AVENUE OF THE AMERICAS
NEW YORK, NY 10036		   X   X   Chairman of the Board and CEO  

Signatures

 George C. Barry for John B. Hess   04/09/2008
**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 sales of shares set forth herein are made in connection with a selling plan dated March 20, 2008 that is intended to comply with Rule 10b5-1(c).
(2) This amount includes 305,000 shares held in escrow pursuant to the Corporation's Second Amended and Restated 1995 Long-Term Incentive Plan. The reporting person has only voting power of these shares until the lapsing of the period set by the Committee administering the Plan at which time the shares plus accrued dividends will be delivered to the reporting person if he is still an employee of the Corporation.

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