LOL...as far as I know it comes from my youth in the 60's. The Beatles were first called the Fabulous Four and then it was shortened to the Fab Four.
People could look absolutely "fab" The show was "fab".......yet something tells me I am wrong and it probably comes from being.....

A fragment of an immunoglobulin molecule formed when the moleclule is digested by papain and containing one antigen binding site, one complete light chain and part of one heavy chain also called fab fragment.