In former times, if a person wanted to fight another person, the person would put a chip of wood on his shoulder and dare the other personto knock it off. If the second person knocked it off, that meant he accepted the challenge and was willing to fight. That custom existed among young boys, even in my youth. So, if you have a chip on your shoulder, it is a kind of challenge to anyone to argue with you.

"A chip on your shoulder" means: A perceived grievance or sense of inferiority.

It means that the person who "has a chip on his/her shoulder" is easily irritated and ready to fight.

To have a chip on ones shoulder is a figurative statement in english - meaning that a person has something to prove. Someone who is considered an underdog would behave as though they had a chip on their shoulder. Usually helping someone perform above expectations

The entire history of the expression is listed here: http://en.wikipedia.org/wiki/Chip_on_shoulder Not surprising, like many of our idioms in english, it originates from the Royal Navy =)