have a monkey on (one's) back
1. slang To have a drug addiction. Did you hear? Pete checked himself into rehab because he has a monkey on his back.
2. slang To have a burden. I have such a monkey on my back right now with this project—I can't wait for it to be over.
have a monkey on your back
1 have a burdensome problem. 2 be dependent on drugs. informal Sense 2 originated as mid 20th-century US slang; it can also mean ‘experience withdrawal symptoms after ceasing to take a drug’.