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(Bc) = (0.4-0.7) ps, the dominant mechanism being the decay of the charm constituent.