The polarization of τ leptons produced m e+e- + τ +τ-(y) is measured using a sample of 8977 z+r - paars collected near the peak of the Z ° resonance A polanzatlon of -0 132 4- 0 026 (stat) 4- 0 021 (syst) is determined Thts corresponds to a ratm of the vector to the axial-vector couphng constants of the z lepton to the weak neutral current of T gv/gAeff = 0 0694-0 017 This leads to a value of the effective sm 2 0w at the Z° resonance of sin 2 0eff = 0 23264-0 0043