Durham made his major league debut on May 27, 1980 with the St. Louis Cardinals. He was traded that off-season to the Cubs for Bruce Sutter, and his career took off. He hit 10 home runs and drove in 55 runs in a strike-shortened 1981 season, then followed that with a stellar 1982 season in which he had a .312 batting average with 22 homers, 90 RBI, and 28 stolen bases. He won the Silver Slugger Award as the Cubs' left fielder and made the All-Star team. He followed that with a hot first half in 1983 of 12 homers and 55 RBI and another All-Star Game appearance, but was injured shortly after the break and missed the rest of the season.