We study the sensitivity of the LHC, with 20 fb(-1) of data, to lepton flavor-violating Higgs boson decays h -> tau(+/-)mu(-/+) (and h -> tau(+/-)e(-/+)). We consider the large population of Higgses produced in gluon fusion, combined with leptonic decays of the tau, and estimate that the LHC could set a 95% confidence level bound BR(h -> tau(+/-)mu(-/+)) < 4.5 x 10(-3). This corresponds to a coupling of the order of the Cheng-Sher ansatz y(tau mu) = root m(tau)m(mu)/nu(2). DOI: 10.1103/PhysRevD.86.111701
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