I asked someone with plastics and molding knowledge. His answer was soaking in solvents, which would work for something metal, but you would end up disolving the chip as well.

The other alternative would be grinding away until you get close to the chip, then using dental tools to remove more material and finally dental picks.

Problem with a plastic chip is that it bonds to the "lucite" or resin.

If it becomes one, and is bonded to the chip, I'd say No Way.