This makes me think of a deadeye, used in sailing for the rigging of ships--and perhaps that is the case. (Deadeyes with just one hole are called bull's eyes.) Or perhaps it is just a beautiful product of nature. Whatever the case, this wood is old, and very weathered (I'm inclined to say petrified or fossilized but I'm not completely sure if technically so) and it makes for a very very satisfying object both to look at and to hold.
4 3/4" x 3 7/8" x 1", hard and strong and sound, with a surface worn smooth and nice weight to it.