Ask any local where to try your first real deep-dish pizza and they'll say "Giordanos." It's obviously the best in town. Chicago-style pizza is unique and totally different than what you'll find in Italy. More like a pie, the crust is tall and ingredients are packed in. Give in to trying one slice and you may never want another kind of pizza again.
Pizzas take a while to make, but it's all part of the experience!