The tau lepton lifetime is measured using four different methods with the DELPHI detector. Three measurements using one prong decays are combined, accounting for correlations, resulting in tau(tau) = 298 +/- 7 (stat.) +/- 4 (syst.) fs while the decay length distribution of three prong decays gives tau(tau) = 298 +/- 13 (stat.) +/- 5 (syst.) fs. The combined result is tau(tau) = 298 +/- 7 fs. The ratio of the Fermi coupling constant from tau decay relative to that from muon decay is found to be 0.985 +/- 0.013, compatible with lepton universality.