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 (Last) (First) (Middle) C/O HESS CORPORATION, 1185 AVENUE OF THE AMERICAS 3. Date of Earliest Transaction (Month/Day/Year) 07/13/2006 (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 07/13/2006   J(1)   315,846 (2) D $ 0 0 I See Note (3) Common Stock, $1.00 par value 07/13/2006   J(1)   53,240 A $ 0 1,923,737 (4) D (5)

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 C/O HESS CORPORATION 1185 AVENUE OF THE AMERICAS NEW YORK, NY 10036	X	X	Chairman of the Board

Signatures

George C. Barry for John B. Hess		07/13/2006
**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)	Distributed from a previously reported trust. 53,240 shares were distributed to the reporting person and 262,606 shares were distributed to a trust as to which the reporting person has no reporting obligations under Rule 16.
(2)	Reflects additional 210,564 shares paid as a stock dividend in connection with a 3 for 1 stock split effected on May 31, 2006.
(3)	Held by a previously reporting trust established by the reporting person for the benefit of himself and his children. The reporting person is trustee of the trust.
(4)	Reflects additional 1,246,998 shares paid as a stock dividend in connection with a 3 for 1 stock split effected on May 31, 2006.
(5)	This amount includes 630,000, of which 420,000 shares included in footnote 4 above were paid as a stock dividend in connection with the stock split referred to therein, 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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