  In this work, we examine the process at the LHC in which a Higgs boson is
produced in association with a t t-bar pair and subsequently decays to a pair
of muons. We show that the statistical significance for the discovery of a
light, Standard-Model Higgs boson with a mass around 120 GeV in this channel is
comparable to those for other processes (gluon fusion, weak-boson fusion) in
which the Higgs decays to a muon pair. Combining all three of these channels,
we show that evidence for a Higgs boson with a mass in the range 115 GeV < m_h
< 130 GeV could be obtained at the 3 sigma significance level with an
integrated luminosity of 300 fb^{-1}. We also calculate the enhancement factor
to the cross-section that would be needed to discover a non-standard Higgs
boson in this channel.
