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