  We present a factorization formula for the inclusive production of the Higgs
boson at large transverse momentum $P_T$ that includes all terms with the
leading power of $1/P_T^2$. The cross section is factorized into convolutions
of parton distributions, infrared-safe hard-scattering cross sections for
producing a parton, and fragmentation functions that give the distribution of
the longitudinal momentum fraction of the Higgs relative to the fragmenting
parton. The infrared-safe cross sections and the fragmentation functions are
perturbatively calculable. The most important fragmentation functions are those
for which the fragmenting parton is the top quark, gluon, $W$, $Z$, and the
Higgs itself. We calculate the fragmentation functions at leading order in the
Standard Model coupling constants. The factorization formula enables the
resummation of large logarithms of $P_T/M_H$ due to final-state radiation by
integrating evolution equations for the fragmentation functions. By comparing
the cross section for the process $q\bar{q}\to H t\bar t$ from the
leading-power factorization formula at leading order in the coupling constants
with the complete leading-order cross section, we infer that the error in the
factorization formula decreases to less than 5\% for $P_T>600$ GeV at a future
$100$ TeV collider.
