This Letter presents the first search for a heavy particle decaying into an e ± μ(-/+) final state in sqrt[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 λ(311)' = 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.