Okay, thanks.
The "cheap freewheel" comments make the most sense to my ear. The chain problems suggested (tight link, tight chain, poor lube, etc) could probably make clunking noises, but probably not with beats synced so perfectly to crank rotations.
So ... is it worth fixing right away? In other words, does it cause any problem other than annoyance? Or should I just ride it until it wears out and upgrade when that time comes?