  We study the observability of the $h\to \mu^+\mu^-$ decay in the Standard
Model and the MSSM at the LHC. The observation of the $h\mu\mu$ coupling is
important to determine whether the Higgs particle that generates mass for the
weak bosons is also responsible for mass generation of the second generation of
fermions. We find that the signal via the gluon fusion channel is comparable to
that from the weak-boson fusion. By combining these two channels, observing
$h\to \mu^+\mu^-$ is feasible at the LHC with a delivered luminosity of $300
fb^{-1}$ at $3\sigma$ statistical significance for 110 GeV $<m_h<140$ GeV in
the Standard Model. This corresponds to a $h\mu\mu$ coupling determination at
about 15% accuracy assuming $ht\bar t, hb\bar b$ couplings SM-like. The
observation becomes more promising in the MSSM for $\tan\beta>8$ and $M_A<130$.
