I'm not sure about which dish in Chicago is the most famous, but here's some highly recommended faves. Suppose you're skinny and you need to put on a nice layer of lard round your middle, then try the Malnati Chicago Classic which has a delicious buttery crust to its pizza base, oodles of creamy cheese laid on rich sweet tomato and then with a layer of lean sausage patty atop.
This will also help build your fat up: the traditional Chicagan cheesecake, chocolate-covered with criss-cross icing. The Italian meat sandwich is Illinois in general, perhaps, rather than just Chicago. To a Brit's eyes, it looks and sounds disgusting, but here goes: in a long sub you put in slices of beef, then load it up with giardiniera (spicy vegetable stuff). Then, top with as much juice as possible until the sandwich is totally soaked. (Ugh!)