  Solid He4 is viewed as a nearly perfect Debye solid. Yet, recent calorimetry
indicates that its low-temperature specific heat has both cubic and linear
contributions. These features appear in the same temperature range ($T \sim
200$ mK) where measurements of the torsional oscillator period suggest a
supersolid transition. We analyze the specific heat to compare the measured
with the estimated entropy for a proposed supersolid transition with 1%
superfluid fraction. We find that the experimental entropy is substantially
less than the calculated entropy. We suggest that the low-temperature linear
term in the specific heat is due to a glassy state that develops at low
temperatures and is caused by a distribution of tunneling systems in the
crystal. It is proposed that small scale dislocation loops produce those
tunneling systems. We argue that the reported mass decoupling is consistent
with an increase in the oscillator frequency as expected for a glass-like
transition.
