The lifetime of the τ lepton is measured using the process e+ e- → τ+ τ- , where both τ leptons decay to 3πν(τ). The result for the mean lifetime, based on 711 fb(-1) of data collected with the Belle detector at the ϒ(4S) resonance and 60 MeV below, is τ=(290.17±0.53(stat)±0.33(syst))×10(-15) s. The first measurement of the lifetime difference between τ+ and τ- is performed. The upper limit on the relative lifetime difference between positive and negative τ leptons is |Δτ|/τ<7.0×10(-3) at 90% C.L.