  We investigate the total inclusive decay rate of the (ground state) $B_c$
meson within the framework of an operator product expansion in inverse powers
of the heavy quark masses and subsequent matching onto nonrelativistic QCD. The
expansion is organized as a series in the strong coupling and in powers of the
heavy quark velocities in the $B_c$, reflecting the nonrelativistic nature of a
heavy-heavy bound state. In this aspect the character of the expansion differs
from the more familiar case of heavy-light mesons. The framework incorporates
systematically corrections to the leading $b$- and $c$-quark decays due to
binding effects, as well as contributions from weak annihilation and Pauli
interference. Based on this approach we find for the $B_c$ meson lifetime
$\tau_{B_c}=(0.4 - 0.7)\,$ps, the dominant mechanism being the decay of the
charm constituent.
