  The existence of large \nu_\mu-\nu_\tau mixing suggests the likelihood of
large smuon-stau mixing in supersymmetric models, leading to \mu and \tau
number violation. In addition to interesting signatures in slepton and
neutralino production and decay, this will lead to rare \tau decays, such as
\tau --> mu \gamma. Recently, it has been pointed out that the \tau --> 3\mu
branching ratio could be substantial in the large \tan\beta region of parameter
space, due to an induced \mu-\tau-Higgs vertex. In this paper, another
signature, \tau --> \mu \eta is considered. In the large \tan\beta region, it
is shown that the branching ratio of \tau --> \mu \eta is 8.4 times the
branching ratio of \tau --> 3\mu, independent of any unknown parameters, and it
will thus give the most stringent bound on Higgs-mediated lepton flavor
violation, and may provide its first signature. In the other regions of
parameter space, where \tau --> \mu \gamma is the most prominent decay, the
branching ratio for \tau --> \mu \eta is always substantially lower.
