May 14, 2019

Securities and Exchange Commission

100 F Street, N.E.

Washington, D.C. 20549

Re: Old Dominion Freight Line, Inc.

Ladies and Gentlemen:

Pursuant to General Instruction 7 to Form 3 (Initial Statement of Beneficial Ownership), Form 4 (Statement of Changes in Beneficial Ownership) and Form 5 (Annual Statement of Changes in Beneficial Ownership) promulgated by the Securities and Exchange Commission (the “Commission”) pursuant to Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), the undersigned director, officer and/or shareholder of Old Dominion Freight Line, Inc. (the “Company”) hereby authorizes and designates David S. Congdon, Ross H. Parr, Adam N. Satterfield and Wendy U. English, and each of them, to execute and file with the Commission on the undersigned’s behalf any and all statements on Form 3, Form 4 or Form 5 relating to the undersigned’s beneficial ownership of securities of the Company as required by Section 16(a) of the Exchange Act and the rules of the Commission promulgated thereunder. This authorization and designation shall be effective for so long as the undersigned remains subject to the provisions of Section 16 of the Exchange Act.

Effective as of the 14^th day of May, 2019.

/s/ Bradley R. Gabosch

Bradley R. Gabosch

Gabosch Bradley R 4