Then in 1947, he hitchhiked with Dennis Weaver, his best friend at the university, to New York City, where he landed the role of Turk in Come Back, Little Sheba.

[3] Chapman's first role on television was in 1951 on the series Starlight Theatre, playing the part of an arrogant high-school football player in an episode titled "Miss Bruell".

[5] Some of the other series in which Chapman appeared in supporting roles or as a guest star include Gunsmoke, Harbourmaster, The Rifleman, The Lloyd Bridges Show, The Everglades, Decoy, Dundee and the Culhane, Mission: Impossible, Storefront Lawyers, Quincy, M.E., The A-Team, The Virginian, Matlock, NYPD Blue, Bonanza and Murder, She Wrote.

Between 1972 and 1975, he guest-starred in three episodes of NBC's McCloud, which starred his friend Dennis Weaver, whom Chapman had originally urged to go into show business.

During his lengthy career, his appearances include roles in East of Eden (1955), Baby Doll (1956), The Birds (1963), The Cowboys (1972), Where the Red Fern Grows (1974), Norma Rae (1979), 52 Pick-Up (1986) and Reindeer Games (2000).

[4] Plays that he wrote included The Buffalo Skinner (1958), Cry of the Raindrop (1960), Hoot Sudie (1970), Go Hang the Moon (1974), Night at the Red Dog (1979), and Happy Days Are Here Again Blues (1979).