We present the first measurement of the left-right cross-section asymm
etry (A(LR)) in Z-boson production observed at the SLAC Linear Collide
r. In 1992 the SLD detector recorded 10 224 Z events produced by the c
ollision of longitudinally polarized electrons with an unpolarized pos
itron beam at a center-of-mass energy of 91.55 GeV. The average electr
on beam polarization during the run was (22.4 +/- 0.6)%. We measure A(
LR) to be 0.100 +/- 0.044 (stat.) +/- 0.004 (syst.), which determines
the effective weak mixing angle to be sin2 theta(W)eff = 0.2378 +/- 0.
0056 (stat.) +/- 0.0005 (syst.).