I dont think Chicago style food goes hand in hand with a sports bar here in LA. I frequent Barneys Beanery in WeHo and there is a heavy chitown clientele there..... If you are thinking of Joe's in Wicker Park, its not happening guy.......
There is a bar on Lincoln in Santa Monica just outside of Venice, very dingy, used to be called The Bitter Redhead now called Nocturnal. Full of rowdy Bears fan and they grills brats and burgers outisde. Always a good time for the game.
Might be a little late for you, but Tin Horn Flats on Magnolia in Burbank is a huge Chicago sports bar. Not sure about food there, but they will definitely have the Bears on.