I don't mean to quibble too much, but the original Monsters of the Midway were the University of Chicago's football team. The midway is the mile-long park that stretches north-south between 59th and 60th streets and Cottage Grove Ave and Stony Island (east-west); it bisects the U of C's campus. Wikipedia's got an article here: http://en.wikipedia.org/wiki/University_of_Chicago

The Chicago Bears coopted the U of C football team's nickname and insignia, that stylized "C" on their helmets.