Thigpen was selected by the Chicago White Sox in the fourth round of the 1985 amateur draft. He made the major leagues the next August and moved into the White Sox's closer role. After two straight 30-save seasons, Thigpen had the best season of his career in 1990, setting the then-major league record of 57 saves (his record was eclipsed by Francisco Rodríguez when he made 62 saves in 2008). He also maintained a 1.83 ERA and was named to the AL All-Star team. He also blew eight saves that season, including two three-run leads.