  The total cross section for Higgs production in bottom-quark annihilation is
evaluated at next-to-next-to-leading order (NNLO) in QCD. This is the first
time that all terms at order alpha_s^2 are taken into account. We find a
greatly reduced scale dependence with respect to lower order results, for both
the factorization and the renormalization scales. The behavior of the result is
consistent with earlier determinations of the appropriate factorization scale
for this process of mu_F ~ M_H/4, and supports the validity of the bottom
parton density approach for computing the total inclusive rate. We present
precise predictions for the cross section at the Tevatron and the LHC.
