fat chance
slim chance

He would play dead, though it was a slim chance at best.

Even the slim chance that such success is possible kept Sales going.

There may be just one slim chance if I can get back in that time.

It was a slim chance, but one which had to be tried.

Even a slim chance was better than not looking at all.

It is a slim chance, at best, but the only one I have.

But there was a slim chance it might not be.

Alone he at least had a chance, however slim it might turn out to be.

But for the East, it is still a slim chance.

He had to at least try to give them that one slim chance, though.