I would recommend Freddy's Pizzeria on South 61st Avenue. It is actually considered to be in the Cicero neighborhood but it is the best pizza around. Once you go here you will never want to have pizza anywhere else.
I don't know of a lot of pizza joints there, but it's Chicago, so there's probably more than I know of. Regardless, the best I've had is Barney's Pizza. It's simple, but it's pizza, so that's a good thing.