  We present a precise measurement of the left-right cross section asymmetry
($A_{LR}$) for $Z$ boson production by $\ee$ collisions. The measurement was
performed at a center-of-mass energy of 91.26 GeV with the SLD detector at the
SLAC Linear Collider (SLC). The luminosity-weighted average polarization of the
SLC electron beam was (63.0$\pm$1.1)%. Using a sample of 49,392 $\z0$ decays,
we measure $A_{LR}$ to be 0.1628$\pm$0.0071(stat.)$\pm$0.0028(syst.) which
determines the effective weak mixing angle to be $\swein=0.2292\pm0.0009({\rm
stat.})\pm0.0004({\rm syst.})$.}
