From Longman Dictionary of Contemporary Englishhave a chip on your shoulderhave a chip on your shoulderUNFAIRto easily become offended or angry because you think you have been treated unfairly in the past → chip
Examples from the Corpus
have a chip on your shoulder• In some cases folks are just mad and have a chip on their shoulder.• The Doyle kid has had a chip on his shoulder ever since his mom and dad divorced. 