1. I said good morning to Ed and he snapped back at me. He sure has a chip on his shoulder today.
2. Carl has a chip on his shoulder because he was passed over for promotion in favor of Maria, although he feels he was better qualified.

The sense of personal injustice is usually imagined. The expression originates from the custom of placing a chip on one’s shoulder and daring another person to knock it off as a way of challenging someone to fight.