  We use lattice QCD to predict the mass of the $B_c$ meson. We use the MILC
Collaboration's ensembles of lattice gauge fields, which have a quark sea with
two flavors much lighter than a third. Our final result is
$m_{B_c}=6304\pm12^{+18}_{- 0} MeV$. The first error bar is a sum in quadrature
of statistical and systematic uncertainties, and the second is an estimate of
heavy-quark discretization effects.
