Chapman was born and raised in Chicago and then studied theatre at the University of Michigan. His first published work was a story to Analog Science Fiction and Fact in 1969. As a rule his work is more fable-like in tone and surreal than is common for that magazine. He also had several stories in Damon Knight's Orbit (anthology series). He has primarily been published in small literary magazines since the late 1970s. A collection of his stories was titled Dossier.