The lifetime of the tau lepton is measured using data collected in 1994 by the L3 detector at LEP. The precise track position information of the Silicon Microvertex Detector is exploited. The tau lepton lifetime is determined from the signed impact parameter distribution for 30322 tau decays into one charged particle and from the decay length distribution for 3891 tau decays into three charged particles. Combining the two methods we obtain ττ = 290.1 ± 4.0 fs.