A native of Union Springs, Alabama, Chapman graduated from Alabama School of Fine Arts in 1983 with the Duane Dushion Award and the Prix d’excellence de Danse Award. After dancing for Alabama Ballet for one season, Chapman joined American Ballet Theatre (ABT) in 1984 by invitation of Mikhail Baryshnikov as a member of the corps de ballet. He was promoted to soloist in 1987 and to principal dancer in 1989. With ABT, Chapman performed all the leading roles in the ballet repertoire and in works by many of the twentieth century’s master choreographers, including George Balanchine, Agnes de Mille, Jiri Kylian, Fredrick Ashton, Mats Ek, Twyla Tharp, Mark Morris, Merce Cunningham and Antony Tudor. He also created leading roles in Clark Tippet’s Bruch Violin Concerto No. 1 and Twyla Tharp’s The Elements. Chapman has appeared in Dance in America, the film Dancers and the documentary Ballet, as well as numerous television shows and was featured on national news broadcasts. In 1993, he joined the Bavarian National Ballet as a principal dancer before returning to ABT in 1995. Chapman appeared with Hamburg Ballet, English National Ballet, Teatro Colon in Buenos Aires and Finnish National Ballet as a guest star.

In 1996, Chapman was named Artistic Director of Alabama Ballet. During his leadership, the company grew from 16 to 44 professional and apprentice dancers. He also founded the Alabama Ballet School, the apprentice pre-professional training program, Alabama Ballet Summer Program and Gorham’s Bluff Summer Residency.