The Green Bay Packers were formed in 1919, and were granted a franchise in the newly formed NFL on August 27, 1921.
However, at the end of the 1921 season, the Packers franchise was revoked when Chicago Staleys (now Bears) owner George Halas informed the league that the Packers had paid three college players (Hunk Anderson, Ojay Larson, and Hec Garvey from Notre Dame) to appear in their final game of the season, marking the beginning of the Bears/Packers rivalry.
Packers founder Curly Lambeau appealed to the league, and the franchise was reinstated, although Lambeau was required to pay the $50 league entry fee to do so.
Interestingly, all three players would go on to play for the Bears in their pro careers. Anderson would play for the Bears, and be their head coach from 1942-45. Larson would play for the Bears in 1922 (and 1929), and the Packers again in 1925. And Garvey played for the Bears in 1922-23.