Using approximately 1.3 fb(-1) of data collected by the D0 detector between 2002 and 2006, we measure the lifetime of the Bc+/- meson in the Bc-/+-->J/psimicro+/-+X final state. A simultaneous unbinned likelihood fit to the J/psi+micro invariant mass and lifetime distributions yields a signal of 881+/-80(stat) candidates and a lifetime measurement of tau(Bc+/-)=0.448(-0.036)(+0.038)(stat)+/-0.032(syst) ps.