This is a way to ask a question very hesitantly. Use it when you want to ask a question, even though you're pretty sure that the answer is "no". For example:

I hear a bit of an accent. Are you from Michigan, by any chance?

A: Where'd you go to school? B: Penn State. A: Oh, really? A good friend of mine went there. Do you know Keiko Ishihara, by any chance?