  We propose a many-body wave function that exhibits both diagonal and
off-diagonal long-range order. Incorporating short-range correlations due to
interatomic repulsion, this wave function is shown to allow condensation of
zero-point lattice vibrations and phase rigidity. In the presence of an
external velocity field, such a perfect crystal will develop non-classical
rotational inertia, exhibiting the supersolid behavior. In a sample calculation
we show that the superfluid fraction in this state can be as large as of order
0.01 in a reasonable range of microscopic parameters. The relevance to the
recent experimental evidence of a supersolid state by Chan and Kim is
discussed.

Statistical Mechanics;Superconductivity