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.
After high school he toured with Ray Charles (1959–1962), Art Farmer's and Benny Golson's Jazztet (1962), and Sonny Rollins. He took part in two classic Jackie McLean albums in the early 1960s, One Step Beyond and Destination Out, to which he also contributed the bulk of compositions and which led to two influential albums of his own for Blue Note Records, Evolution (1963) with Jackie McLean and Lee Morgan, and Some Other Stuff (1964) with Herbie Hancock and Wayne Shorter.