  We compute analytic results for the QCD corrections to Higgs boson production
via gluon fusion in hadronic collisions in the limit in which the top quark is
much heavier than the Higgs boson. The first non-leading corrections of
$\O(\alpha_s^3 \mh^2/m_t^2)$ are given and numerical results presented for both
LHC and SSC energies. We confirm earlier numerical results showing that the
dominant corrections have the same mass dependence as the Born cross section.
