The term means to interact in a provocative way, daring someone to resist you. When you are angry at someone, and instead of speaking about it, you do something to annoy them in hopes that they will argue with you, you’ve got a chip on your shoulder. Proactive Passive Aggression.
to be touchy, to be easily provoked (During the 19th century, a person in the united states would challenge others to a fight by placing a wooden chip on his/her shoulder and daring them to knock it off, and if the other person did so, the fight was on.)