Chapman is probably best known by basketball fans because of one particular moment: during the 1997 NBA Playoffs in the first round, the Phoenix Suns, up two games to one, were trailing the Seattle SuperSonics by three points with seconds to go in game four at America West Arena in Phoenix. With the ball seemingly on its way out of bounds, Chapman saved it and threw up a three-pointer, making the shot with 2.2 seconds left and sending the game into overtime. Despite this miraculous play, the Suns ended up losing the game, and the deciding game 5, and were eliminated from the playoffs. Chapman has declared publicly he does not like to be reminded of the moment too much because the Suns still lost. On informal polls made by the NBA and NBA teams among fans, however, that moment often comes out as one of the top moments in league history.
A high school basketball star 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.
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. He could not help the Hornets win many games, however, as the expansion team went 20-62 that year.
During the 1989-1990 season, Chapman, whose matinee idol looks helped increase his popularity in North Carolina, entered the NBA all star dunk competition. Despite performing a two hands and two balls dunk stunt, he lost to dunking legend Dominique Wilkins in the competition. Chapman averaged 17 points per game that year, but the Hornets were not much better than a year earlier. After one-and-a-half more seasons with the Hornets, Chapman was traded midway through the 1991-1992 season to the Washington Bullets. He was injured, however, and could only participate in the final game of the season. This would turn out to be the first of a number of injuries that gave Chapman trouble during the rest of his career.
Chapman returned to the Bullets in the 1992-1993 season for 65 games at restored health. He played 60 games during the 1993-1994 season and 45 games during the 1994-1995 season. He had his second major injury during the latter season, after which he was traded to the Miami Heat. By the time Chapman was with the Heat, he was losing his hair considerably, a fact that later on helped him take the decision to shave off his head hair completely and sport a bald look. Chapman averaged 14 points per game that year, but he was placed on the injured list again and only participated in 56 games. After that season, he signed with the Suns.
As with many other Suns players, Chapman became a fan favorite upon his arrival in Phoenix for the 1996-1997 season. He played in 65 games, and scored 13 points per game. His popularity in Phoenix was enhanced by the game tying shot in game four of the 1996-1997 season first round playoffs against the Supersonics.
Chapman played 68 games during the 1997-1998 season for the Suns, scoring almost 16 points per game. But he would be injured again during the strike shortened 1999 season, playing 38 games.
Chapman would play 53 games during the 1999-2000 season, but he became re-injured and decided to retire from the NBA then.
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 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.
Chapman and his wife now make their offseason home in Lexington, Kentucky, and own a restaurant there.
In an article in the Lexington Herald-Leader newspaper in October of 2005 Chapman told the paper that while he was a student at the University of Kentucky he was told by the school not to date African-American girls.