A high school basketball star at Apollo High in Owensboro, Kentucky, Chapman was heavily recruited by many universities. He chose, however, to stay close to home when he signed with the University of Kentucky. Chapman was a star at Kentucky, named All-SEC during his freshman and sophomore years and scoring 1,073 points in only two years.

After two years with Kentucky, Chapman was selected with the 8th overall pick in the 1988 NBA Draft and became the first player ever signed by the Charlotte Hornets in the franchise's history. Chapman was popular among basketball fans in Charlotte, as he averaged 16.9 points per game his first season there.

Chapman played a total of 666 regular season NBA games, scoring 9,731 points for an average of 14.6 points per game, with 1,798 assists for an average of 2.7 assists per game, and 1,645 rebounds, for 2.5 rebounds per game.

After retiring from active play Chapman remained with the Phoenix Suns, first as a scout and later as Director of Basketball Operations. For the 2004 and 2005 NBA Playoffs, he served as a color commentator on TNT. In 2005, he moved from Phoenix to accept a personnel scout position with the Minnesota Timberwolves. In 2006, he accepted the position of vice president of player personnel with the Denver Nuggets.