From Longman Dictionary of Contemporary Englishfat chancefat chanceinformalBELIEVE used to say that something is very unlikely to happenfat chance of ‘You can go to bed now and sleep easy.’ ‘Fat chance of that!’ → fat
Examples from the Corpus
fat of• There is fat chance of that for as long as the Government allows the banks to carry on with their grasping one-way policy. 