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
(Last)
(First)
(Middle)
C/O HESS CORPORATION, 1185 AVENUE OF THE AMERICAS		 3. Date of Earliest Transaction (Month/Day/Year)
10/26/2006
(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

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
7.00% Mandatory Convertible Preferred Stock (1) 10/26/2006   J     450,000 11/25/2003 12/01/2006 Common Stock (2) $ 50 0 I See Note (3)
7.00% Mandatory Convertible Preferred Stock (1) 10/26/2006   J(4)   450,000   11/25/2003 12/01/2006 Common Stock (2) $ 50 450,000 I See Note (5)

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   10/30/2006
**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) If the reporting person exercises his option to convert the preferred stock into common stock prior to the maturity date, he will receive 2.4915 shares of common stock for each share of preferred stock converted. If the preferred stock is converted at maturity, it will automatically convert into between 2.4915 and 3.0897 shares of common stock per share of preferred stock, depending on the applicable market value of the common stock.
(2) 450,000 shares of convertible preferred stock convert into a minimum of 1,121,175 shares of common stock and a maximum of 1,390,365 shares of common stock.
(3) Distributed from previously reported trust.
(4) Acquired by trust referred to in Note 5.
(5) Held by a trust newly established for the benefit of the reporting person's mother. The reporting person is a co-trustee.

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