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 one’s back
tv. to have a drug addiction. (Drugs. Have got can replace have.) Gert has a monkey on her back.