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 * 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) 03/28/2007 (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 03/28/2007   S(1)   200 D $ 57.26 11,588,779 I Charitable Lead Annuity Trust (2) Common Stock, $1.00 par value 03/28/2007   S   100 D $ 56.72 11,588,679 I Charitable Lead Annuity Trust (2) Common Stock, $1.00 par value 03/28/2007   S   200 D $ 56.89 11,588,479 I Charitable Lead Annuity Trust (2) Common Stock, $1.00 par value 03/28/2007   S   100 D $ 56.91 11,588,379 I Charitable Lead Annuity Trust (2) Common Stock, $1.00 par value 03/28/2007   S   100 D $ 56.78 11,588,279 I Charitable Lead Annuity Trust (2) Common Stock, $1.00 par value 03/28/2007   S   100 D $ 56.83 11,588,179 I Charitable Lead Annuity Trust (2)

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
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		03/29/2007
**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)	The sales of shares set forth herein are made in connection with a selling plan by the charitable lead annuity trust referred to below dated August 1, 2006, as amended February 5, 2007, that is intended to comply with Rule 10b5-1(c).
(2)	Held by a previously reported charitable lead annuity trust established under the will of Leon Hess. The reporting person is one of five trustees of the trust.

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