  The prospects at the CERN LHC are investigated for the discovery via decays
into muon pairs of neutral Higgs bosons in the minimal supergravity model.
Promising results are found for the CP-odd pseudoscalar ($A^0$) and the heavier
CP-even scalar ($H^0$) Higgs bosons at large $\tan\beta \equiv v_2/v_1$. For
$\tan\beta \agt 10$ and 100 GeV $\alt m_A,m_H \alt$ 550 GeV, the $A^0$ and the
$H^0$ masses could be precisely reconstructed from the dimuon invariant mass.
