U Sco is a recurrent nova as well as a double-lined eclipsing binary. As such, an accurate orbital period before its next eruption can be combined with a measured period after that eruption to yield a dynamical measurement of the ejected mass. A properly phased radial velocity curve for both components could yield the mass of the white dwarf, which theory strongly predicts to be near the Chandrasekhar mass. Radial velocity measurements from three epochs were available but until now could not be phased together reliably. Both programs require a highly accurate orbital period. We report on eclipse photometry from 1988 to 1994 with times for nine eclipses. The eclipse light curve is variable in shape and asymmetric with the egress slower than the ingress, implying a bright and variable hot spot. We derive an orbital period of 1.2305631 +/- 0.0000030 days and an eclipse minimum time of HJD 2,447,717.6061 +/- 0.0032. Phasing the radial velocity data shows a large scatter in both the emission- and absorption-line velocities, which have significantly different averages. This casts doubt on previous mass determinations for the white dwarf, in particular the claim that the white dwarf is much less than the Chandrasekhar mass.