Warren in Lancaster, PA
There are a lot of species of boxwood (genus Buxus) native from England to Japan. There is variation in form, shrub to small tree, but the species I have seen have similar wood.

If I were going to use native wood for chess pieces I would try dogwood and persimmon. Both are dense and fine grained; both have a terrific luster off the tool.
Persimmon is not common in Pennsylvania, but there are records from Adams and Allegheny counties (and others).