Born in Inman, South Carolina, Chapman was an ensign in the United States Navy during World War II, from 1943 to 1946.

[2] He received a Bachelor of Science degree from the University of South Carolina in 1945, and a Bachelor of Laws from University of South Carolina School of Law in 1949.

Chapman was elected as chairman of the South Carolina Republican Party on July 22, 1961,[3] and served until he resigned on February 15, 1963.

His service terminated on October 2, 1981, due to elevation to the Fourth Circuit.

[2] Chapman was nominated by President Ronald Reagan on July 16, 1981, to a seat on the United States Court of Appeals for the Fourth Circuit vacated by Judge Clement Haynsworth.