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Specific heat measurements from 2 to 300 K of hydrogenated amorphous silicon prepared by hot-wire chemical vapor deposition show a large excess specific heat at low temperature, significantly larger than the Debye specific heat calculated from the measured sound velocity. The as-prepared films have a Schottky anomaly that is associated with metastable hydrogen in the amorphous network, as well as large linear and excess cubic term commonly associated with tunneling two-level systems in amorphous solids. Annealing at 200 °C, a temperature that enables hydrogen mobility but not evaporation, irreversibly reduces the heat capacity, eliminating the Schottky anomaly and leaving a reduced linear heat capacity. A non-monotonic dependence on growth temperature and H content is observed in all effects, except for sound velocity, which suggests that the tunneling two-level systems and the Schottky anomaly are associated with atomic hydrogen and require low density regions to form, while sound velocity is associated with the silicon network and increases with increasing growth temperature.