I like the ideas of many of you out there, but you have to keep the material in mind. On Mohs scale ivory has a hardness of 2.5. That's about the same as fingernails, amber, and silver. Chert/flint is much more common and it has a hardness of ~7.

Given the size my best guess is that it is the base of some art/religious piece. Of course that's always the line used when archaeologists don't know what something is.