Any guesses as to what this is?

It has a steel split beam, a brass knurl that slides up to bring the ends together for holding something, and the handle is wood.

Found it at the flea market amongst some misc. hand tools.

Looks like a hot rivet holder.

a handle to hold barbed wire while you nail it to a wooden post?

Whatever it is, I love it!! Thanks for posting!!

Thanks for the replies so far. The photos are very trimmed down to fit, but you can see against the tape measure it's just about 4-5/16" long

Someone has identified this as a pin vise. There is a hollow section down the center, so that makes perfect sense. Thanks. Now to try it out.

Fancy looking ones like that one were typically used by jewelers and watchmakers.  I have had a few like that one, but not for awhile.

I would agree it's a pin vise. Here's mine that I got in a shop in way upstate NY. In good shape if you overlook the split in the handle.
It's almost a twin to the one 3 bay posted, except for a few subtle differences.

Mike

cool Tools.

Really like that piece.  Maybe the side hole is for setting small nails/brads?