After reading the Wikipedia article I was wondering about a possible connection between these two idioms.
Quoted from Wikipedia: Chip on shoulder
This idiom traces its roots back to a custom that was known in North America since the early 19th century. The New York newspaper Long Island Telegraph reported on 20 May 1830 "when two churlish boys were determined to fight, a chip [of wood] 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 8 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".
This is not related to the question: What are the origins for the phrases "Knock it off" and "Cut it out"? I am enquiring about the connection between two distinct idioms, one being:
To have a chip on one's shoulder
The other being:
Knock it off
It looks to me like they might both originate from the same source!