  We report low temperature ($T$) heat capacity ($C$) data on a
multiple-quantum-well GaAs/AlGaAs sample in the quantum Hall regime. Relative
to its low field magnitude, $C$ exhibits up to 10^5-fold enhancement near
$\nu$=1 where Skyrmions arethe ground state of the confined two-dimensional
electrons. We attribute the large $C$ to a Skyrmion-induced, strong coupling of
the nuclear spin system to the lattice. The data are consistent with the
Schottky nuclear heat capacity of Ga and As atoms in the quantum wells, except
at very low $T$ where $C$ vs $T$ exhibits a remarkably sharp peak suggestive of
a phase transition in the electronic system.
