  The transverse momentum distribution of the Higgs at large $P_T$ is
complicated by its dependence on three important energy scales: $P_T$, the top
quark mass $m_t$, and the Higgs mass $m_H$. A strategy for simplifying the
calculation of the cross section at large $P_T$ is to calculate only the
leading terms in its expansion in $m_t^2/P_T^2$ and/or $m_H^2/P_T^2$. The
expansion of the cross section in inverse powers of $P_T$ is complicated by
logarithms of $P_T$ and by mass singularities. In this paper, we consider the
top-quark loop contribution to the subprocess $q\bar{q}\to H+g$ at leading
order in $\alpha_s$. We show that the leading power of $1/P_T^2$ can be
expressed in the form of a factorization formula that separates the large scale
$P_T$ from the scale of the masses. All the dependence on $m_t$ and $m_H$ can
be factorized into a distribution amplitude for $t \bar t$ in the Higgs, a
distribution amplitude for $t \bar t$ in a real gluon, and an endpoint
contribution. The factorization formula can be used to simplify calculations of
the $P_T$ distribution at large $P_T$ to next-to-leading order in $\alpha_s$.
