Forster rapidly ascended to the big league level, making the White Sox's opening day roster in 1971 after only 10 games at the single-A level in the minor leagues. He recorded a 3.99 ERA and hit .400 (2 for 5) as a 19-year-old. He became Chicago's top relief pitcher in 1972 and saved 29 games, which ranked second in the American League that season. After splitting time between the bullpen and the starting rotation in 1973, Forster returned primarily to the bullpen in 1974 and led the American League in saves with 24. He then missed most of 1975 with an arm injury, which allowed teammate Rich Gossage to become the league leader in saves that season.