Those places may have great pizza, but I would have to side with the members who voted Wholly Joe's as authentic Chicago pizza. I lived in Chicago in the 1970's. Back then, no one outside Chicago really knew what Chicago-style pizza pie (we called it that) was.
Wholly Joe's has regular, extra thin, and deep dish. Deep dish is the Chicago style I remember from my Chicago days. I'd call ahead because it takes extra baking time.
The pic says it all:
http://whollyjoes.com/index.php?option=com_content&view=article&id=34&Itemid=8