Person attended Brantley High School in Brantley, Alabama and wasn't heavily recruited, but Auburn took a chance on him in 1982. Person was mostly a reserve forward his freshman year, but saw more playing time as the year progressed. In his sophomore season, Person was a full-time starter at forward and teamed with junior Charles Barkley to form a potent inside-outside combination. Person's superb outside shooting skills (unusual for a big man) and Barkley's inside play helped Auburn University to its first ever NCAA tournament appearance in 1984. Person averaged 19.1 points per game that season.
After Barkley left for the NBA, Person became the unquestioned leader of a young Auburn team that wasn't expected to do much in 1984-85. He averaged 22.5 points per game and set the Auburn single-season record for total points scored (747). Auburn was a seventh seed (out of 10) in the SEC Tournament that season, but Person and freshmen Chris Morris, Jeff Moore, and Terrence Howard helped Auburn to become the first team to win four games in four days in the tournament and to win its first-ever SEC Tournament championship. Person was an Honorable Mention All-America selection that season. In the NCAA tournament, Auburn upset Kansas and Purdue before bowing out in the Final 16 to North Carolina.
Person returned better than ever for his senior season and averaged 21.5 points per game and led the Tigers back to the NCAAs. Auburn upset No. 1-ranked St. John's University on its way to an Elite Eight appearance before losing to eventual champion Louisville. Person earned his second straight All-America Team selection.
Selected fourth in the 1986 NBA Draft out of Auburn University by the Indiana Pacers, the small forward won the Rookie of the Year award in 1987 and played six seasons with Indiana. During this time, Person established a reputation as a brash, trash talking antagonist who, for better or worse, brought a competitive spirit to a floundering Pacers franchise. This culminated during the 1991 and 1992 playoffs when Person had an ongoing rivalry with Hall of Famer and future Pacers President Larry Bird.
Person was traded in 1992, along with Micheal Williams, to the Minnesota Timberwolves in exchange for Sam Mitchell and Pooh Richardson. After his contract expired in 1994, he signed free agent contracts with the San Antonio Spurs, Charlotte Hornets and Seattle SuperSonics. He was traded by the Spurs with a conditional first-round draft pick and other considerations to the Chicago Bulls for Steve Kerr on January 22 1999 but was immediately waived.
Person was nicknamed as "The Rifleman" not only for his prolific long-range shooting but because he was named after the American actor Chuck Connors, star of the TV series The Rifleman. Over his career, Person played in 943 games, with averages of 14.7 points per game, 5.1 rebounds per game, a 45.8 field goal percentage, and 36.2 three point shooting percentage. He ranks 17th all-time in career three-point field goals made.
He is currently an assistant coach with the Sacramento Kings.