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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1. Name and Address of Reporting Person * Gordon Shearer   2. Issuer Name and Ticker or Trading Symbol HESS CORP [HES] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) Senior Vice President (Last) (First) (Middle) C/O HESS CORPORATION, 1185 AVENUE OF THE AMERICAS 3. Date of Earliest Transaction (Month/Day/Year) 05/08/2007 (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 05/08/2007   A   4,000 A $ 0 34,000 D (1)

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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

Option to purchase Common Stock

$ 58.14

05/08/2007

A

4,000

05/08/2008

05/08/2017

Common Stock, $1.00 par value

4,000

$ 0

4,000

D

Option to purchase Common Stock

$ 58.14

05/08/2007

A

4,000

05/08/2009

05/08/2017

Common Stock, $1.00 par value

4,000

$ 0

4,000

D

Option to purchase Common Stock

$ 58.14

05/08/2007

A

4,000

05/08/2010

05/08/2017

Common Stock, $1.00 par value

4,000

$ 0

4,000

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
Gordon Shearer C/O HESS CORPORATION 1185 AVENUE OF THE AMERICAS NEW YORK, NY 10036			Senior Vice President

Signatures

George C. Barry for Gordon Shearer		05/10/2007
**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)	These shares are 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 lapsing of the period and other conditions 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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