Grachan Moncur III (born June 3, 1937) is an American jazz trombonist. He is one of the few real free jazz trombonists, as well as a prolific composer. He is the son of jazz bassist Grachan Moncur II and the nephew of jazz saxophonist Al Cooper.
Born in New York City and raised in Newark, New Jersey, Grachan began playing the cello at age nine, and switched to the trombone at eleven. In high school he attended the Laurinburg Institute in North Carolina, the private school where Dizzy Gillespie had studied. While still in school he began sitting in with touring jazz musicians on their way through town, such as Art Blakey and Jackie McLean, with whom he formed a lasting friendship.