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 ν=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

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... s, except at very low T where C vs T exhibits a remarkably sharp peak suggestive of a phase transition in the electronic system.