Gamma(Hto bbar{b}) to order αα_s

We compute the decay rate of the Standard Model Higgs boson to bottom quarks to order $\alpha\alpha_s$. We apply the optical theorem and calculate the imaginary part of three-loop corrections to the Higgs boson propagator using asymptotic expansions in appropriately chosen mass ratios. The corrections of order $\alpha\alpha_s$ are of the same order of magnitude as the ${\cal O}(\alpha_s^3)$ QCD corrections but have the opposite sign.