What story had actual physical monkeys on people's backs?

Was chatting with my friend about the latest wacky invention from Japan, a monkey-looking robot backpack feeding the wearer tomatoes and I commented that it reminded me of a vaguely recalled old story about monkeys on people’s back. When my friend wanted to know more, all I could find with Google was references to the proverbial monkeys, drug abuse and such. I still remain 98% sure there’s at least one well-known such story out there, possibly in “One Thousand and One Nights”. Any Dopers know what I’m talking about?

Not quite a monkey but The Burr Woman otherwise fits.

The Sinbad story is similar, but it’s the Old man of The Sea, not a monkey. That’s likely what you’re remembering.

That does sound likely yes. Thanks!

There’s “The Monkey Treatment” by George R.R.Martin