“Did I leave my camera at your place, by any chance?”
You can't find your camera. Last week, you took it to a friend's apartment. You wonder if you left it there, so you call and ask this.
Did I leave my camera at your place, by any chance?
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In casual conversation, you can call someone's house their "place":
You have a really nice place!
Do you want to come over to my place for dinner?
You can also call a restaurant a "place":
(question), by any chance?
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?