We report a high precision measurement of the τ-lepton lifetime using data collected with the Belle detector at the ϒ(4S) resonance and 60 MeV below. We measure the τ lifetime to be τ = (290.17 ± 0.53(stat.) ± 0.33(syst.)) ⋅ 10-15 s, which is almost twice more precise than the current world average. We also set the upper limit on the relative lifetime difference between positive and negative τ leptons to be |ττ+−ττ−/τaverage|<7.0×10−3 at 90% CL. This is a first measurement on this quantity.