The Mott insulator is accepted as the appropriate ground manifold for the strongly interacting Fermion Hubbard model, with solid He-3 as the simplest exemplar. It is a manifold because of the spin degrees of freedom, which order antiferromagneticallly due to atom exchange, below a critical temperature. No corresponding effect of exchange has been known for the Bose solid. I show that in fact the Bose-Hubbard model solid has a corresponding manifold of phase degrees of freedom which can conduct particle currents and which exhibit an ordering transition. The possible applicability to the observed "supersolidity" phenomena in solid He-4 will be discussed.