If you have access to it, a magnetic pin tumbler is a miracle worker when it comes to cleaning up this kind of stuff. Alternatively a vibratory tumbler with the right media can work as well just not as fast and more of a pain.
Layne
Use the tumbler or make sure you are ready to lose a finger, have the chain destroyed, and perhaps have fragments of the chain shrapnel embedded in your forehead...
Haven't lost my own finger to that mistake, but knew a jeweler who did.
But I will admit to having some bits of chain stuck in my forehead when I was just a puppy... that's how you learned NOT to do stuff in those days.