On April 26, 1967, Concannon was traded to the Chicago Bears along with a 1968 fourth round pick (#106-Alan Bush), in exchange for future hall of fame tight end Mike Ditka. The transaction was intended to fill roster vacancies created by the retirements of Eagles' tight end Pete Retzlaff and Bears' quarterback Rudy Bukich. In three seasons with the Eagles, Concannon recorded 103 passes for 637 yards (43.7%), 4 passing touchdowns, 8 interceptions, 50 carries for 433 yards (8.7-yard avg.), 2 rushing touchdowns and the team was 3-0 in his starts.
In 1967, he was named the starter at quarterback, leading the team to a 7-6-1 record, which would be George Halas' final year as an NFL head coach. Concannon appeared in 13 games (12 starts), recording 92-of-186 completions (49.5%), 1,260 yards, 6 touchdowns and 14 interceptions, while rushing for a career-high 279 yards and 3 touchdowns.