First Measurement of the Left-Right Charge Asymmetry in Hadronic {ital Z} Boson Decays and a New Determination of sin{sup 2}{ital {theta}}{sup eff}{sub {ital W}}

We present the first measurement of the left-right charge asymmetry A{sup obs}{sub Q} in hadronic Z boson decays. This was performed at E{sub c.m.}=91.27 GeV with the SLD at the SLAC Linear Collider with a polarized electron beam. Using 89838 events we obtain A{sup obs}{sub Q}=0.225{plus_minus}0.056{plus_minus}0.019, which leads to a measurement of the electron left-right asymmetry parameter, A{sub e}=0.162{plus_minus}0.041{plus_minus}0.014, and sin{sup 2} {theta}{sup eff}{sub W}=0.2297{plus_minus}0.0052{plus_minus}0.0018. Also, the A{sup obs}{sub Q} measurement combined with the left-right cross section asymmetry determines A{sub e} independent of the value of the electron-beam polarization. {copyright} {ital 1996} {ital The American Physical Society}