Chapin was born on March 9, 1957 in Manchester, Connecticut. He attended Phillips Academy in Andover, Massachusetts where he studied classical music and jazz. In the late 1970s he attended the Hartt School of Music at the University of Hartford in Connecticut, studying with saxophonist Jackie McLean. In 1980 he graduated from Rutgers University where he studied with saxophonist Paul Jeffrey, pianist Kenny Barron and guitarist Ted Dunbar. From 1981 to 1986 he toured with Lionel Hampton as lead saxophonist and musical director. He performed with Chico Hamilton's band from 1988 to 1989.