1
general::
Phrase(s): fat chance
Fig. very little likelihood. • Fat chance he has of getting a promotion. • You think she’ll lend you the money? Fat chance!
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Very little or no possibility, as in A fat 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.
American Heritage Idioms