The coupling of the Z boson to quarks is studied in a sample of about 3.5 million hadronic Z decays collected by the L3 experiment at LEP from 1991 to 1995. The forward-backward quark charge asymmetry is measured by means of a jet charge technique. From the measured asymmetries, the effective weak mixing angle is determined to be sin(2)(w) = 0.2327 +/- 0.0012(stat,) +/- 0.0013(syst.). (C) 1998 Published by Elsevier Science B.V. All rights reserved.