Well two things... There are more than one kind of "chip bully" and certain kinds are a payday for you. Others... well you need to be very careful.
Your perception of what "chip bully" means is important here.
Most loose aggressive players can be beat by being patient and absolutely NOT letting them get under your skin.
But sometimes it's just better to pick up your chips and go to another table.
Getting the idea that I should "pay him back" or "teach him a lesson" has certainly come into my mind. And fairly often has ended with me suffering.
In fact, when you are up against a drunk maniac who raises everything and wont fold you can get hurt. But if you hold tight, weather the losses, and encourage him to stay and continue his "amazing run" you will win it back and more by picking the good spots and playing him. Traps are good and so are passive calls... but be careful with the raises it might shut him down.
That is another point, you might check your own aggression. Don't let these guys wig you out post flop. Just enter with the good cards, then PLAY BACK at him. Sometimes these guys are easy to
bluff.
But again... why not go somewhere softer when these guys get under your skin? There are only like 10,000 tables right now.
cAPS