  We investigate the prospects for the discovery at the CERN Large Hadron
Collider of a neutral Higgs boson produced with one bottom quark followed by
Higgs decay into a muon pair. We work within the framework of the minimal
supersymmetric model. The dominant physics background from the production of $b
\mu^+\mu^-$, $j\mu^+\mu^-$, j=g,u,d,s,c, and $b {\bar b} W^+W^-$ is calculated
with realistic acceptance cuts. Promising results are found for the CP-odd
pseudoscalar ($A^0$) and the heavier CP-even scalar ($H^0$) Higgs bosons with
masses up to 600 GeV. This discovery channel with one energetic bottom quark
greatly improves the discovery potential of the LHC beyond the inclusive
channel $pp\to \phi^0\to \mu^+\mu^- +X$.
