The E158 experiment at SLAC has made the first measurement of parity violation in electron-electron (Moller) scattering. We report a preliminary result using 50% of the accumulated data sample for the right-left parity-violating cross-section asymmetry (APV) in the elastic scattering of 45 and 48 GeV polarized electron beams with unpolarized electrons in a liquid hydrogen target. We find APV = (-160 +- 21 (stat.) +- 17 (syst.)) parts per billion, with a significance of 6.3sigma for observing parity violation. In the context of the Standard Model, this yields a measurement of the weak mixing angle, sin^2(thetaW-MSBAR)(Q^2 = 0.026 GeV^2) = 0.2379 +- 0.0016 (stat.) +- 0.0013 (syst.). We also present preliminary results for the first observation of a single-spin transverse asymmetry in Moller scattering.