The exact quote was “What if one person could actually own another’s mind, in a new and more complete form of slavery?”
It's fun to have a list of mind control in sf, but none of the nominees (with the possible exception of Necropolis, which I haven't read) seem to quite meet the specs.
I'm assuming chattel slavery-- public, socially acceptable, and including a market. For it to be a more complete slavery, there's presumably surveillance, and probably the ability to make modifications.
It's entirely possible that I'm over-extrapolating and/or that such slavery was brought up as a story possibility in a class discussion rather than being based on an actual story.
Silverberg's To Live Again comes close, though the angle was more about fear of an individual slave revolt and there was no ability to modify.
A Fire Upon the Deep comes close, but the people with Focus mostly seem to be government property, with only one sub rosa case of personal use.
The Blight and the Puppet Masters aren't people.
There's another Vinge story ("The Cookie Monster"?) niggling at my memory about AIs wiggling their way out of repetitious VR, but even that doesn't quite meet the specs. IIRC, it was one scientist rather than the whole social structure-- it was rather in the spirit of Sturgeon's "Microcosmic God".
More generally, slavery is really common in sf and I've never seen a general discussion of it.
And symbolically, trying to control, modify, and sometimes own other people's minds is something people try to do a lot.