  The lifetime of the $B_c^+$ meson is measured using semileptonic decays
having a $J\!/\!\psi$ meson and a muon in the final state. The data,
corresponding to an integrated luminosity of $2\mathrm{~fb^{-1}}$, are
collected by the LHCb detector in $pp$ collisions at a centre-of-mass energy of
$8\,\mathrm{TeV}$. The measured lifetime is $$\tau = 509 \pm 8 \pm 12
\mathrm{~fs},$$ where the first uncertainty is statistical and the second is
systematic.
