  We present a new measurement of the left-right cross section asymmetry (ALR)
for Z boson production by e+e- collisions. The measurement was performed at a
center-of-mass energy of 91.28 GeV with the SLD detector at the SLAC Linear
Collider (SLC). The luminosity-weighted average polarization of the SLC
electron beam was (77.23+-0.52)%. Using a sample of 93,644 Z decays, we measure
the pole-value of the asymmetry, ALR0, to be
0.1512+-0.0042(stat.)+-0.0011(syst.) which is equivalent to an effective weak
mixing angle of sin**2(theta_eff)=0.23100+-0.00054(stat.)+-0.00014(syst.).
