Here they are in order of my recommendation.
Giordano’s - Probably the best if you’re only going to do one. Their stuffed pizza is classic Chicago and incredibly delicious.
Lou Malnati’s - My personal favorite, but not quite the iconic Chicago style. A little thinner than the others.
Gino’s - Often recommended and often disappointing, IMO. Cheese tends to be rubbery. Sauce too much like Chef Boyardee. However, this is the most touristy spot, and has a pretty good atmosphere.
Uno’s/Due - Pretty good, but doesn’t hold a candle to Giordano’s or LM’s. Claims to have invented Chicago style pizza, but this is hotly disputed.
Noteworthy, but not really Chicago style:
Piece - Makes a good New Haven style. Great beer selection.
Peaquad’s - Best standard style in the city. Not too expensive.