I agree with an earlier poster that you should try to squeeze a Bulls chip in there somewhere, but it creates a chip color problem.
You have something like:
You end up with a Blackhawks and Bulls chip that are too similar to differentiate. If you use black as the dominant color with the Bulls, you run into a differentiation problem b/w Bulls and Bears. You have to go with the dark blue/black Bears chip otherwise you run into the same "two chips with dominant red color" problem b/w Bears and Blackhawks.
I suppose you could do a Bears chip that used orange as the primary color (the Bears have worn that as an alt jersey), but that doesn't resonate as strongly to me as the traditional dark blue. Still, if you did orange Bears, then you could do black Bulls and keep the red/pink Blackhawks.