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 THOMAS JOSEPH
2. Issuer Name and Ticker or Trading Symbol

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

_____ Director                    _____ 10% Owner
__X__ Officer (give title below)    _____ Other (specify below)
VICE PRESIDENT
(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  17974 (1)A$0 17974 D  
Common Stock (restricted) 3/16/2020  M  17974 D$0 0 D  
Common Stock 3/16/2020  M  17974 A$0 192049 D  
Common Stock 3/16/2020  F  7604 D$79.85 184445 D  
Common Stock         96007 I By grantor retained annuity trust 
Common Stock         66709 I By Irrevocable Trust 
Common Stock         31671 I By wife 
Common Stock         55280 I By wife as trustee (2)(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   5795.1     (5) (5)Common Stock 5795.1 $86.28 154872 D  

Explanation of Responses:
(1) Performance share units (awarded on March 16, 2017) earned and vested as of March 16, 2020.
(2) The reporting person disclaims beneficial ownership of these shares, and this report shall not be deemed an admission that the reporting person is the beneficial owner of these shares for purposes of Section 16 or for any other purpose.
(3) These shares are held in trusts, for the benefit of the reporting person's children, of which his wife is a trustee.
(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 THOMAS JOSEPH
2850 GOLF ROAD
ROLLING MEADOWS, IL 60008-4002


VICE PRESIDENT

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

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