Wiktionary
n. An abbreviated form of snowball's chance in hell.
Wikipedia
Snowball's Chance, is a parody of George Orwell's Animal Farm written by John Reed, in which Snowball the pig returns to the Manor Farm after many years' absence, to install capitalism — which proves to have its own pitfalls.
Usage examples of "snowball's chance".
And frankly, Your Majesty, we don't have a snowball's chance of getting him out of there.
Maybe Carlos will change his mind, though I think there's a snowball's chance of that.
But it didn't take much waking thought to arrive at the conclusion that there was only one way-only one possible way-that gave us a snowball's chance in hell of getting out of the lens.
You'd think that'd be one time when the devil didn't stand a snowball's chance in hell.
If it didn't fall right off onto the floor when you tipped the shelf up, it probably slid to a place where you haven't got a snowball's chance in hell of getting hold of it.