We derive the mass of the white dwarf in the eclipsing recurrent nova U Sco from the radial velocity semi-amplitudes of the primary and secondary stars. Our results give a high white dwarf mass of M1 = 1.55 +/-0.24 Modot, consistent with the thermonuclear runaway model of recurrent nova outbursts. We confirm that U Sco is the best Type Ia supernova progenitor known, and predict that the time to explosion is within ~700,000 years.