What do you mean by "Fat Chance" ?

It means that there is almost no chance of something happening. It is not an overly respectful expression, personally I rarely use it unless with close friends or if the conversation is jokey. I also use it to refer to myself, like "I knew i should have studied before going out, but like, fat chance of that." to mean that there is little chance i would study rather then going out with friends.

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.

answers.com

It is a good example of saying the opposite of what is meant.

Fat means plentiful or probably here. But the opposite is meant, so it actually means lean, thin, improbable.

So it means "not likely", just the opposite of "fat chance".

I encourage people not to say things that have to be taken as their opposites to be understood correctly. But this is a very common custom of people and it is done as it is a cute way to avoid being criticised for saying something truthful yet unacceptable for whatever reason. It is better to avoid opposite meaning phrases if you can do it as it helps make you clearer.

talking of chance, it can be numerically known in relation to its frequent occurences (eg. number games)

in nature, no, there is no place for chance as it happens naturally

Meaning yourself is an ace idea

not going to happen or no chance or impossible

I dont know but it sounds interesting

Nada, Never, Not in your lifetime, No.

It's like finding that needle in the haystack. <}:-})