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 *

GALLAGHER J PATRICK JR
2. Issuer Name and Ticker or Trading Symbol

Arthur J. Gallagher & Co. [ AJG ]
5. Relationship of Reporting Person(s) to Issuer (Check all applicable)

__X__ Director                    _____ 10% Owner
__X__ Officer (give title below)    _____ Other (specify below)
President & CEO
(Last)          (First)          (Middle)

2850 GOLF ROAD
3. Date of Earliest Transaction (MM/DD/YYYY)

3/13/2020
(Street)

ROLLING MEADOWS, IL 60008-4002
(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 (restricted) 3/16/2020  A  56158 (1)A$0 56158 D  
Common Stock (restricted) 3/16/2020  M  56158 D$0 0 D  
Common Stock 3/16/2020  M  56158 A$0 143211.2368 D  
Common Stock 3/16/2020  F  23755 D$79.85 119456.2368 D  
Common Stock         205965 I By Corporation 
Common Stock         66703 I By Irrevocable Trust 
Common Stock         246538 I By Spouse (2)
Common Stock         219897 I By Trust (3)

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
Phantom Stock  (4)3/13/2020  I   17385.4     (5) (5)Common Stock 17385.4 $86.28 139196.5 D  

Explanation of Responses:
(1) Performance share units (awarded on March 16, 2017) earned and vested as of March 16, 2020.
(2) Shares held in revocable trust of which my spouse is sole Trustee and as to which I disclaim beneficial ownership.
(3) Held in trust for benefit of children.
(4) Each share of phantom stock represents a right to receive one share of Gallagher common stock.
(5) These shares represent awards under the Age 62 Plan, a nonqualified deferred compensation plan of the Company, which have been deemed invested in Company common stock at the election of the reporting person. Participants vest in these awards when they attain age 62, or after a one-year period for participants who have attained age 61.

Reporting Owners
Reporting Owner Name / Address
Relationships
Director10% OwnerOfficerOther
GALLAGHER J PATRICK JR
2850 GOLF ROAD
ROLLING MEADOWS, IL 60008-4002
X
President & CEO

Signatures
/s/ April Hanes-Dowd, by power of attorney3/17/2020
**Signature of Reporting PersonDate

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