  We compute the three-loop QCD corrections to the vertex function for the
Yukawa coupling of a Higgs boson to a pair of bottom quarks in the limit of
vanishing quark masses. This QCD form factor is a crucial ingredient to
third-order QCD corrections for the production of Higgs bosons in bottom quark
fusion, and for the fully differential decay rate of Higgs bosons to bottom
quarks. The infrared pole structure of the form factors agrees with the
prediction from infrared factorization in QCD.
