I, like any others, have had people who have busted my chops at one time or another. Maybe I had it coming; maybe not. This saying often refers to someone who is harassing or bugging you. It is also used to describe a potentially deserved tongue lashing for wrongdoings. While this may be frustrating to put up with, it also makes me wonder how this strange saying came into being.
At the turn of the century, it was fashionable for a man to wear long sideburns; these hairy things became known as mutton chops or lamb chops; due to their meat-like resemblance.
When a man got hit in the face, he was literally being hit in the chops; thus someone was busting his chops. These men perhaps, were the unfortunate bearers of the first chops’ busting. Being that long mutton chops are no longer in style (thank the Flying Spaghetti Monster – bless his noodly appendages, for this), this saying is no longer used in the literal sense.