Chapman was born in Leicester and was raised in Melton Mowbray. He enjoyed science, acting and comedy and, after graduating from Emmanuel College, Cambridge and St Bartholomew's Hospital Medical College, he turned down a career as a doctor to be a comedian instead. Chapman eventually established a writing partnership with John Cleese, which reached its critical peak with Monty Python during the 1970s. He subsequently left Britain for Los Angeles, where he attempted to be a success on American television, speaking on the college circuit and producing the pirate film "Yellowbeard" (1983), before returning to Britain in the early 1980s.