  We report a measurement of the parity-violating asymmetry in fixed target
electron-electron (Moller) scattering: A_PV = -175 +/- 30 (stat.) +/- 20
(syst.) parts per billion. This first direct observation of parity
nonconservation in Moller scattering leads to a measurement of the electron's
weak charge at low energy Q^e_W = -0.053 +/- 0.011. This is consistent with the
Standard Model expectation at the current level of precision:
sin^2\theta_W(M_Z)_MSbar = 0.2293 +/- 0.0024 (stat.) +/- 0.0016 (syst.) +/-
0.0006 (theory).
