fat chance

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fat chance (uncountable)

1. (idiomatic, colloquial, sarcastic) Little or no chance, a low or nonexistent likelihood of occurrence or success.
   • 1970 June 8, Tom Wolfe, “Radical Chic: That Party at Lenny's”, in New York Magazine‎:

     As soon as the word comes out of your mouth […] your own servant is going to size you up as one of those limousine liberals, or whatever epithet they use, who are busy pouring white soul all over the black movement, and would you do as much for the white lower class, for the domestics of the East Side, for example, fat chance, sahib.

   Fat chance that I’ll ever go back to Swansea.

• a fat lot
• no chance, not a chance, chance'd be a fine thing