Born in Highland Park, Illinois, Chapman earned a bachelor's degree in English Literature from Princeton University in 1941, and an honorary master's degree from Harvard in 1956.[1] During World War II he was stationed in Morocco and Europe while working for United States Navy intelligence with the rank of lieutenant.[4][5] After the war, he taught briefly on the faculty of Princeton University before accepting a position as an instructor in the Department of Dramatic Arts at the University of California, Berkeley, where he worked from 1948 to 1950.[1][4]
In 1950 Chapman joined the faculty at Harvard University as an Assistant Professor of English, and was later promoted to Associate Professor in 1956 and a Professor of English Literature in 1967.[4] Some of the courses he taught at the university were classes on George Bernard Shaw, Restoration drama, and a course entitled "Drama Since Ibsen".[1] His notable pupils included André Bishop, Tommy Lee Jones, John Lithgow, Arthur Kopit, and John Updike.[1] From 1960 to 1980 he was director of the Loeb Drama Center for Harvard University and Radcliffe College.[1] He retired from Harvard University in 1989.[1]
As a playwright, Chapman's most successful work was an adaptation of Herman Melville's Billy Budd which he co-authored with Louis O. Coxe, a fellow faculty member at Princeton.[4][1] The first version of their play, entitled Uniform of Flesh, debuted Off-Broadway at the Lenox Hill Theatre in 1949.[6] The two men revised the work significantly, and retitled it Billy Budd for the work's staging on Broadway in 1951.[1] While the work was financially unprofitable, it was a critical success; winning the Donaldson Award for Best First Play and the Outer Critics Circle Award for Best Play in 1951.[2][3] The British actor Sir Peter Ustinov adapted the play into a film in 1962.[7]
Chapman's other plays included The General, Hero, and The Troublesome Tourist.[4] In addition to his work as a teacher and playwright, he served as an advisor to the Juilliard School in its organization and planning of its drama school at the Lincoln Center for the Performing Arts.[8]
Chapman died at the age of 81 on September 27, 2000, in Fort Lauderdale, Florida, where he had lived since his retirement from Harvard.[1][4]