 After the 1983 season Stoddard was traded by Baltimore to the Oakland Athletics for third baseman Wayne Gross.In spring training (March 26, 1984) he was again traded, this time to the Chicago Cubs for two minor league players.During the 1984 season, Stoddard pitched in 58 games and posted a 10-6 record and seven saves as the Cubs won the National League East title—their first postseason appearance since the 1945 World Series.