Moye joined the innovative, avant-garde quintet, the Art Ensemble of Chicago (AEC), in 1969 and he has been a permanent member ever since. Moye and the other members of AEC draw their influence from both Africa and the Caribbean, rural as well as urban spaces - the whole spectrum of black music. Their radically experimental performances include painted faces, costumes and exotic instruments, which all contribute to their energetic improvisations. In addition to his work with AEC, Moye has been a member of The Leaders since 1984 and has recorded with the Black Artists Group, Joseph Jarman, Don Pullen, Cecil McBee, Hamiet Bluiet, Julius Hemphill, Chico Freeman and Lester Bowie's Brass Fantasy. He also leads the Sun Percussion Summit, a group dedicated to exploring the traditions of African American percussion music.
His recordings have won him the praise of critics at such esteemed publications as Rolling Stone, Down Beat, Melody Maker, The New York Times, Audio Magazine and Stereo Review. He was the winner of the Downbeat International Critics Poll in 1977, 1978 and 1982, and the New York Jazz Poll in 1979 and 1980. He received performance grants from the National Endowment for the Arts in both 1974 and 1981. He lives in Chicago, with his wife, Gloria, and their son, Bongo.