We present the first measurement of the left-right charge asymmetry AQobs in hadronic Z boson decays. This was performed at Ec.m. = 91.27 GeV with the SLD at the SLAC Linear Collider with a polarized electron beam. Using 89 838 events we obtain AQobs = 0.225±0.056±0.019, which leads to a measurement of the electron left-right asymmetry parameter, Ae = 0.162±0.041±0.014, and sin2θWeff = 0.2297±0.0052±0.0018. Also, the AQobs measurement combined with the left-right cross section asymmetry determines Ae independent of the value of the electron-beam polarization.