We study the sensitivity of the LHC, with 20 inverse-fb of data, to lepton
flavour 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 \times 10^{-3}. This correponds to
a coupling of order the Cheng-Sher ansatz y_{tau mu} = sqrt{m_tau m_mu/v^2}.Comment: 6 pages, 4 figures, references adde
