The lifetime of the Bc- meson is measured using 272 exclusive Bc-→J/ψ(→μμ)π decays reconstructed in data from proton-antiproton collisions corresponding to an integrated luminosity of 6.7 fb1 recorded by the CDF II detector at the Fermilab Tevatron. The lifetime of the Bc- meson is measured to be τ(Bc-)=0.452±0.048(stat)±0.027(syst) ps. This is the first measurement of the Bc- meson lifetime in a fully reconstructed hadronic channel, and it agrees with previous results and has comparable precision.