Fat chance means, sarcastically, that there is no chance whatever. Fat chance of that.
It is one of the odd phrases that means the opposite of what it says, since a fat chance is no chance. Slim chance means much the same, which is what makes the pair so strange.
1phrasefat chanceSarcastically, there is no chance whatever.
“Getting the deposit back, fat chance.”
fat chance is a phrase.
Practised in Small Talk & Everyday Phrases