Lou Malnati's has one of the best Chicago style deep dish pizza. It is right there with Gino's East and Pizzeria Due. And you can have it sent to your home using this link:
http://www.loumalnatis.com/About/ship%20it.aspx
I used to have them shipped to friends who moved. Now I will be a recipient. They claim to ship 250,000 pizzas a year.