We used to remove embedded hair from combs, brushes, hair rollers,
etc. by soaking them in a solution of ammonia, water and mild
detergent for about half an hour. The gunk literally floated off,
and whatever was left was easily removed with another comb. Then
everything was rinsed off in plain water and came out clean as a
whistle. If you do soak the chain, try brushing the hair out with
an old toothbrush afterwards.
Dee