I agree with what has been said about the difference between "will" and "be going to" to express future time.
However, I think that the use of a conditional clause changes things a bit. Suppose you're the speaker -the one who is asking the question. If you haven't made up your mind yet about going to Chicago, how can you ask me if I'm going with you or not? In my opinion, the main reason why "be going to" doesn't make much sense in that sentence is the fact that you are still not sure you're going to Chicago. How can you ask me if I'm going with you when you still don't know if you're going yourself?
To me, "be going to" would make sense in a different situation.
"I'm going to Chicago tonight, are you coming with me/ will you come with me?"
but
"If I go to Chicago (tonight), will you come with me?"
Perhaps I'm just too fussy about this.
Miriam