  Kim and Chan have recently observed Non-Classical Rotational Inertia (NCRI)
for solid $^4$He in Vycor glass, gold film, and bulk. Their low $T$ value of
the superfluid fraction, $\rho_{s}/\rho\approx0.015$, is consistent with what
is known of the atomic delocalization in this quantum solid. By including a
lattice mass density $\rho_{L}$ distinct from the normal fluid density
$\rho_{n}$, we argue that $\rho_{s}(T)\approx\rho_{s}(0)-\rho_{n}(T)$, and we
develop a model for the normal fluid density $\rho_{n}$ with contributions from
longitudinal phonons and ``defectons'' (which dominate). The Bose-Einstein
Condensation (BEC) and macroscopic phase inferred from NCRI implies quantum
vortex lines and quantum vortex rings, which may explain the unusually low
critical velocity and certain hysteretic phenomena.
