This idiom or expression means:

Not a good chance. (Is used with a negative verb.)

A. Do you think he has a chance to get admitted to the university at all?
B. He hasn’t got a Chinaman’s chance!!

Also:
Ghost of a chance.
Snowball’s chance in hell.
Chinaman’s chance in hell.

This idiom or expression means:

No way.
Not a chance.

A. They want you to apologize.
B. They want ME to apologize? Fat chance!! There’s no way I’ll apologize to them.

Also see:
Chinaman’s chance.