The diffusion of hydrogen molecules in hexagonal D2O ice (Ih) in the temperature range of 25-60 K was investigated by quasielastic neutron scattering. The observed spectra consist of a narrow elastic peak and a broad quasielastic component. The single-particle diffusion coefficient for H-2 in D2O ice was obtained using a simple model of diffusion and is remarkably high-comparable to;he coefficient of H-2 in a liquid.