The polarization of τ leptons produced in the reaction e+e−→τ+τ− at the Z resonance has been measured using the τ decay modes eνeντ, μνμντ, πντ, ϱντ, and a1ντ. The mean value obtained is Pτ = −0.152±0.045, indicating that parity is violated in the neutral current process e+e− → τ+τ−. The result corresponds to a ratio of a neutral current vector and axial vector coupling constants of the τ lepton and a value of the electroweak mixing parameter sin2θw(M2Z) = 0.2302 ± 0.0058.