During his first season, Mueller averaged 12.7 points per game for the Bulls and earned NBA All-Rookie Team honors. He was traded midway through his second season to the LA Lakers for Jim Barnes and a draft choice on January 9, 1968. Mueller would return to the Bulls for the start of the 68-69 season by way of another trade through the Lakers sending Keith Erickson to LA for Erwin on September 23, 1968. However his tenure in Chicago would not last through the season. On January 31, 1969 Mueller was traded to the Seattle Supersonics for a draft choice and cash.