This Letter presents the first search for a heavy particle decaying into an e±μ∓ final state in √s=7  TeV pp collisions at the LHC. The data were recorded by the ATLAS detector during 2010 and correspond to a total integrated luminosity of 35  pb-1. No excess above the standard model background expectation is observed. Exclusions at 95% confidence level are placed on two representative models. In an R-parity violating supersymmetric model, tau sneutrinos with a mass below 0.75 TeV are excluded, assuming all R-parity violating couplings are zero except λ311′=0.11 and λ312=0.07. In a lepton flavor violating model, a Z′-like vector boson with masses of 0.70–1.00 TeV and corresponding cross sections times branching ratios of 0.175–0.183 pb is excluded. These results extend to higher mass R-parity violating sneutrinos and lepton flavor violating Z’s than previous constraints from the Tevatron.