  We study the interplay of Mott localization, geometric frustration, and
superfluidity for hard-core bosons with nearest-neighbor repulsion on the
triangular lattice. For this model at half-filling, we demonstrate that
superfluidity survives for arbitrarily large repulsion, and that diagonal solid
order emerges in the strongly correlated regime from an order-by-disorder
mechanism. This is thus an unusual example of a stable supersolid phase of
hard-core lattice bosons at a commensurate filling.
