Originally Answered: In the saying "You have a big chip on your shoulder." what kind of chip is it talking about?
Chip on his shoulder:
Meaning - Having a harboured grievance or sense of inferiority and being quick to take offence.
This is reported as originating with the nineteenth century U.S. practise of spoiling for a fight by carrying a chip of wood on one's shoulder, daring others to knock it off. This has more than the whiff of folk-etymology about it, but in fact it is the actual derivation of this phrase. The two earliest printed citations that refer to chips on shoulders bear this out.
Firstly, in 1830 the New York newspaper The Long Island Telegraph printed this:
"When two churlish boys were determined to fight, a chip would be placed on the shoulder of one, and the other demanded to knock it off at his peril."
The actual phrase 'chip on his shoulder' appears a little later, in the Weekly Oregonian 1855:
"Leland, in his last issue, struts out with a chip on his shoulder, and dares Bush to knock it off."
A belligerent attitude or grievance, as in Mary is easily offended; she always has a chip on her shoulder. This term actually was defined in a newspaper article (Long Island Telegraph, May 20, 1830): "When two churlish boys were determined to fight, a chip would be placed on the shoulder of one and the other demanded to knock it off at his peril." [Early 1800s]
The saying originated during the nineteenth century in the United States, where people wanting a physical fight would carry a chip of wood on their shoulder, daring others to knock it off. Printed citations of this include the Long Island Telegraph, a New York newspaper, which on May 20th, 1830, printed "When two churlish boys were determined to fight, a chip would be placed on the shoulder of one, and the other demanded to knock it off at his peril."
A similar notion is mentioned in the issue of The Onondaga Standard of Syracuse, New York, on 8th December 1830: “‘He waylay me,’ said I, ‘the mean sneaking fellow — I am only afraid that he will sue me for damages. Oh! if I only could get him to knock a chip off my shoulder, and so get round the law, I would give him one of the soundest thrashings he ever had.’”
Some time later, in 1855, the phrase "chip on his shoulder" appeared in the Weekly Oregonian, stating "Leland, in his last issue, struts out with a chip on his shoulder, and dares Bush to knock it off."
Carrying a chip on one's shoulder was a form of challenge in the same spirit as a medieval knight throwing down his gauntlet. If an opponent picked up the glove, or knocked the chip of wood off their shoulder, the challenge was accepted and the fight was on.
Usage over time changed, now suggesting somebody who shows a belligerent attitude, acting as though they are asking for a fight. The chip is now figurative, but the idea remains the same.
British and Irish meaning
In both countries it also has a meaning of somebody who has a self-righteous feeling of oppression or inferiority which they never miss an opportunity to flaunt. The implication of looking for a fight is less strong. It more implies trying to gain the upper hand through second-hand moral superiority.
In Britain this is often used in the context of a media personality or politician who drones on about their "working class roots" from a position of power and authority.
In Ireland the joke is made about "The well balanced Irishman : a chip on both shoulders". This is somebody who has an endless supply of current and, more often historical, national injustices to whine about. It is quite probable that all these are true, but the fact that they never miss a chance to bring them up, often combined with the fact that they have never suffered these injustices themselves, leaves the person open to satire.
The tenth song in Legally Blonde: The Musical is entitled "Chip On My Shoulder". The song is about the trials of law school and is essentially the turning point of the production.