The tau lepton lifetime is measured with the L3 detector at LEP using the complete data taken at centre-of-mass energies around the Z pole resulting in ττ=293.2±2.0(stat.)±1.5(syst.fs. The comparison of this result with the muon lifetime supports lepton universality of the weak charged current at the level of six per mille. Assuming lepton universality, the value of the strong coupling constant, αs is found to be αs(mτ2) = 0.319 ± 0.015 (exp) ± 0.014 (theory).