If you have little chance of doing something your chances are slim. Makes sense: slim things are smaller than fat ones. It follows, then, that if your chances are great, you have a fat chance, right?
It doesn’t seem to work that way. Slim chance and fat chance seem to be oxymora, for if I say “I have a slim chance of winning” my chances are probably greater than if I say, “Fat chance I have of winning!” This is tantamount to saying I have no chance at all!
There is a syntactic difference which may account for the semantic difference between these two sentences. But even if I make their syntactic structures identical, “I have a fat chance of winning,” I don’t get the impression that my chances are great.
Fat chance is used more often ironically, usually with sarcastic intonation for emphasis. Irony, of course, turns meanings upside-down. “I love you” is pretty straightforward but by simply changing the intonation to, “I, love you?” you turn the meaning around. The same irony converges fat chances with slim chances.
Don’t you wish we had an irony pill that worked the same way on our bodies?