Hargrove graduated from Sewanee Military Academy and Rice University, where he majored in philosophy, studied languages, and was elected to Phi Beta Kappa. He enlisted in the army and served in the European Theater of Operations in IPW Team 138; he was discharged in January 1946 as a Master Sergeant. After the War he became a corporate executive, served as Senior Assistant Postmaster General of the United States, and was appointed U.S. Ambassador to Australia in 1976. After his return, he joined an investment management firm in Houston and served on corporate and non-profit boards.