Pequod's is the best example of Chicago-style I have tried. Lou Malnati's is the best of the chains. The sausage is best at both.
Also, Piece makes a decent New Haven style pizza.
If you want a New York style slice in Chicago, there's only a couple of decent places. One, Armitage Pizzeria in Lincoln Park has an excellent street slice. The owner is a East Coast transplant who used to own a coal-fired place (Coalfire Pizza).