http://www.learnersdictionary.com/search/chance The phrase by any chance is used when asking questions in a polite way. - Are you free tonight, by any chance?If something happens by chance, people have not planned it or tried to make it happen. - By (pure/sheer) chance, I saw him again at the grocery store. - We found the house entirely by chance."By any chance" and "by chance" are not interchangeable, are they?