We report on the first search for electron-muon lepton flavor violation (LFV) in the decay of a b quark and b antiquark bound state. We look for the LFV decay ϒ(3S)→e^{±}μ^{∓} in a sample of 118 million ϒ(3S) mesons from 27 fb^{-1} of data collected with the BABAR detector at the SLAC PEP-II e^{+}e^{-} collider operating with a 10.36 GeV center-of-mass energy. No evidence for a signal is found, and we set a limit on the branching fraction B[ϒ(3S)→e^{±}μ^{∓}]<3.6×10^{-7} at 90% C. L. This result can be interpreted as a limit Λ_{NP}/g_{NP}^{2}>80 TeV on the energy scale Λ_{NP} divided by the coupling-squared g_{NP}^{2} of relevant new physics (NP).