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.