Monkey off my back

Where did the phrase "monkey on/off my back" originate?
Please help, it's driving me insane....

Dictionary of American Slang, 1960:
"monkey on [one's[ back" Drug addiction, considered as a financial, physical, mental, and moral responsibility; the drug habit; lit., a strong addiction that one spends most of one's energy to support. --Common addict use, now universally known. When without drugs an addict feels weighted down and depressed, when buying drugs an addict is supporting pushers and his drug habit, thus, fig., the addict carries an extra burden; it may be a large or small monkey--some have a $100-a-day monkey. Perhaps based on the obs. "have a turkey on one's back."