  The lifetime of the $B_c^{-}$ meson is measured using 272 exclusive
$B_{c}^{-} \to J/\psi (\to \mu^+\mu^-) \pi^-$ decays reconstructed in data from
proton-antiproton collisions corresponding to an integrated luminosity of 6.7
fb$^{-1}$ recorded by the CDF II detector at the Fermilab Tevatron. The
lifetime of the $B_c^{-}$ meson is measured to be $\tau$($B_c^{-}$) = 0.452
$\pm$ 0.048(stat) $\pm$ 0.027(syst) ps. This is the first measurement of the
$B_c^{-}$ meson lifetime in a fully-reconstructed hadronic channel, and it
agrees with previous results and has comparable precision.
