The forward-backward asymmetries for the processes e(+)e(-) --> c (c) over bar and e(+)e(-) --> b (b) over bar at the Z resonance are measured using identified D*(+/-) mesons. In 905,000 selected hadronic events, taken in 1991 and 1992 with the DELPHI detector at LEP, 4757 D*(+) --> D degrees pi(+) decays are reconstructed. The c and b quark forward-backward asymmetries are determined to be: A(FB)(c (c) over bar) = 0.077 +/- 0.029 (stat) +/- 0.012 (sys), A(FB)(b (b) over bar) = 0.059 +/- 0.062 (stat) +/- 0.025 (sys). Constraining the b asymmetry to the value measured by DELPHI using independent analyses, the charm asymmetry is determined to be: A(FB)(c,const) = 0.068 +/- 0.027 (stat) +/- 0.011 (sys). This result corresponds to an effective electroweak mixing angle measured using charm quark events of: sin2 theta(eff)(lept) = 0.2307 +/- 0.0062 (stat) +/- 0.0026 (sys).
