Or, if your stereo has a grounding post, such as your turntable would have (if you're like me and still playing vinyl), you could run a wire from that post to a plumbing pipe.
Thanks for the suggestion. Of course it does! I just ignored it at the outset and have long since forgotten about it.
Having lived for so many years in a world in which nothing was ever grounded and nothing ever came of it (except, perhaps, an inaudible hummm), I tend to be lax, to say the least, about grounding. In fact, I've lived dangerously with electricity my entire life.
(Yup, many times!)
But since we've been on the subject, I've taken the path of least resistance and moved the stereo's plug to the grounded line. (The additional power draw is negligible.)