fat chance

1. Very little or no possibility, as in A fact chance he has of coming in first, or You think they'll get married? Fat chance! A related expression is a fat lot, meaning “very little or none at all,” as in A fat lot of good it will do her. The first of these slangy sarcastic usages dates from the early 1900s, the second from the 1890s.

Example Sentences

My Dad laughed and said something to the effect of “fat chance.”

From Los Angeles Times

Nazir Afzal, a former chief crown prosecutor for North West England, said that many young Asian people who played cricket at home had a "fat chance" of making to professional teams.

From BBC

But fat chance California would do that anyway.

From Los Angeles Times

I hoped that didn't really mean: fat chance.

From Salon

There’s fat chance much of that will carry over into the Gritty meme war.

From The Guardian