This could be just a very, very unique fossil, maybe a game price or something. Not sure. I think it's just too perfect for a fossil. Perfectly round with both sides matching. Pictures of both sides and the rim.
These come up a lot as 'beads' but they're crinoid fossils. Occassionally crinoids were turned into beads but it've never had some ask about one that was a bead. They're always fossils. I have a tupperware container full of them.