Since the NFL created divisions in 1933, the Bears and Packers have always been in the same division, and that is not likely to change before hell freezes over. Until the inclusion of wild-card teams (non-division winners) in the playoffs began 40 years ago, the only way that the two teams could have faced each other in a postseason game would be if they tied for first place in their division and needed an extra contest to settle the issue.
That is precisely what happened in 1941. The Bears won the season opener 25-17 at Green Bay on September 28, but lost to the Packers 16-14 in the season's sixth game on November 2 at Wrigley Field. Both teams ran the table thereafter to finish with identical records of 10-1. A special playoff game was therefore necessary to determine which team would represent the Western Division in the NFL title game against the Eastern-champion New York Giants.
The game was played at Wrigley Field on December 14, one week after the Japanese attack on Pearl Harbor. The Packers struck first. After Bears rookie Hugh Gallarneau fumbled the opening kickoff, Green Bay fullback and future Hall of Famer Clarke Hinkle tallied on a one-yard plunge. Another future Hall of Famer, left end Don Hutson, kicked the extra point. "I just about died," Gallarneau said later, "because [George] Halas was somewhat unforgiving if you made a mistake like that in a Bear-Packer game." (Amazingly, Hinkle's one-yard touchdown carry exceeded the Packers' average for the game, in which their 36 rushing attempts produced only 33 yards.)
Late in the first quarter, Gallarneau redeemed himself with an 81-yard punt return for a touchdown. The extra point was no good, but the Bears more than made up for that by tacking on 24 points in the second quarter. The 30 unanswered points before halftime put the game away, and the Bears coasted to a 33-14 win.
The Bears routed the Giants 37-9 a week later, also at Wrigley Field, to wrap up their second consecutive world championship.
Bears postseason games vs. Green Bay:
1941 - W, 33-14 at Wrigley Field
Bears in NFL championship games:
1933 - W, 23-21 vs. New York Giants
1934 - L, 13-30 at New York Giants
1937 - L, 21-28 at Washington Redskins
1940 - W, 73-0 at Washington Redskins
1941 - W, 37-9 vs. New York Giants
1942 - L, 6-14 at Washington Redskins
1943 - W, 41-21 vs. Washington Redskins
1946 - W, 24-14 at New York Giants
1956 - L, 7-47 at New York Giants
1963 - W, 14-10 vs. New York Giants
Bears in NFC championship games:
1984 - L, 0-23 at San Francisco 49ers
1985 - W, 24-0 vs. Los Angeles Rams
1988 - L, 3-28 vs. San Francisco 49ers
2006 - W, 39-14 vs. New Orleans Saints