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
                                                                                  
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Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934 or Section 30(h) of the Investment Company Act of 1940
                      

1. Name and Address of Reporting Person *

Hill Gregory P.		 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)
COO and President, E&P
(Last)          (First)          (Middle)

HESS CORPORATION, 1185 AVENUE OF THE AMERICAS		 3. Date of Earliest Transaction (MM/DD/YYYY)

5/6/2021
(Street)

NEW YORK, NY 10036
(City)        (State)        (Zip)
4. If Amendment, Date Original Filed (MM/DD/YYYY)

 
 6. Individual or Joint/Group Filing (Check Applicable Line)

_X _ Form filed by One Reporting Person
___ Form filed by More than One Reporting Person

Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security
(Instr. 3) 		2. Trans. Date 2A. Deemed Execution Date, if any 3. Trans. 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 5/6/2021  M(1)  62116 A$0.00 199660 D  
Common Stock, $1.00 par value 5/6/2021  S  32154 D$78.05 (2)167506 D  
Common Stock, $1.00 par value 5/6/2021  S  24134 D$78.82 (3)143372 D  
Common Stock, $1.00 par value 5/6/2021  S  5828 D$79.80 (4)137544 D  
Common Stock, $1.00 par value 5/6/2021  M(1)  58614 A$0.00 196158 D  
Common Stock, $1.00 par value 5/6/2021  S  25823 D$77.96 (5)170335 D  
Common Stock, $1.00 par value 5/6/2021  S  26842 D$78.74 (6)143493 D  
Common Stock, $1.00 par value 5/6/2021  S  5949 D$79.78 (7)137544 D  

Table II - Derivative Securities Beneficially Owned (e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivate Security
(Instr. 3)		2. Conversion or Exercise Price of Derivative Security3. Trans. Date3A. Deemed Execution Date, if any4. Trans. Code
(Instr. 8)		5. Number of Derivative Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4 and 5)		6. Date Exercisable and Expiration Date7. Title and Amount of Securities Underlying Derivative Security
(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)
CodeV(A)(D)Date ExercisableExpiration DateTitleAmount or Number of Shares
Option to purchase Common Stock $51.03 5/6/2021  M     15196  3/6/2018 3/6/2027 Common Stock, $1.00 par value 15196 $0.00 0 D  
Option to purchase Common Stock $51.03 5/6/2021  M     21709  3/6/2019 3/6/2027 Common Stock, $1.00 par value 21709 $0.00 0 D  
Option to purchase Common Stock $51.03 5/6/2021  M     21709  3/6/2020 3/6/2027 Common Stock, $1.00 par value 21709 $0.00 0 D  
Option to purchase Common Stock $48.48 5/6/2021  M     18407  3/6/2019 3/6/2028 Common Stock, $1.00 par value 18407 $0.00 0 D  
Option to purchase Common Stock $48.48 5/6/2021  M     23009  3/6/2020 3/6/2028 Common Stock, $1.00 par value 23009 $0.00 0 D  
Option to purchase Common Stock $48.48 5/6/2021  M     20700  3/6/2021 3/6/2028 Common Stock, $1.00 par value 20700 $0.00 2310 D  
Explanation of Responses:
(1) Common Stock acquired upon exercise of options granted under the Corporation's Long-Term Incentive Plans.
(2) The reported sales transactions were executed at prices ranging from $77.50 to $78.50. The price reported above reflects the weighted average sales price. The reporting person hereby undertakes to provide, upon request, to the SEC staff, the issuer or a security holder of the issuer, full information regarding the number of shares and prices at which the transactions reported on this form were effected.
(3) The reported sales transactions were executed at prices ranging from $78.51 to $79.48. The price reported above reflects the weighted average sales price.
(4) The reported sales transactions were executed at prices ranging from $79.54 to $80.25. The price reported above reflects the weighted average sales price.
(5) The reported sales transactions were executed at prices ranging from $77.45 to $78.40. The price reported above reflects the weighted average sales price.
(6) The reported sales transactions were executed at prices ranging from $78.41 to $79.41. The price reported above reflects the weighted average sales price.
(7) The reported sales transactions were executed at prices ranging from $79.42 to $80.26. The price reported above reflects the weighted average sales price.
Reporting Owners
Reporting Owner Name / Address
Relationships
Director10% OwnerOfficerOther
Hill Gregory P.
HESS CORPORATION
1185 AVENUE OF THE AMERICAS
NEW YORK, NY 10036

COO and President, E&P
Signatures
Barry Schachter for Gregory P. Hill5/7/2021
**Signature of Reporting PersonDate
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