  We report on a precision measurement of the parity-violating asymmetry in
fixed target electron-electron (Moller) scattering: A_PV = -131 +/- 14 (stat.)
+/- 10 (syst.) parts per billion, leading to the determination of the weak
mixing angle \sin^2\theta_W^eff = 0.2397 +/- 0.0010 (stat.) +/- 0.0008 (syst.),
evaluated at Q^2 = 0.026 GeV^2. Combining this result with the measurements of
\sin^2\theta_W^eff at the Z^0 pole, the running of the weak mixing angle is
observed with over 6 sigma significance. The measurement sets constraints on
new physics effects at the TeV scale.
