  Measurements of the moment of inertia by Kim and Chan have found that solid
4He acts like a supersolid at low temperatures. To understand the order in
solid 4He, we have used Path Integral Monte Carlo to calculate the off-diagonal
long range order (ODLRO) (equivalent to Bose-Einstein condensation, BEC). We do
not find ODLRO in a perfect hcp crystal at the melting density. We discuss
these results in relation to proposed quantum solid trial functions. We
conclude that the solid 4He wave function has correlations which suppress both
vacancies and BEC.
