  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 $\Upsilon (3S)\rightarrow e^{\pm}\mu^{\mp}$ in a sample of 118~million
$\Upsilon (3S)$ 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 $\mathcal{B}(\Upsilon(3S)\rightarrow
e^{\pm}\mu^{\mp})<3.6\times10^{-7}\mathrm{at~ 90\%~ CL}$. This result can be
interpreted as a limit $\Lambda_{NP}/g^2_{NP} > 80~$TeV on the energy scale
$\Lambda_{NP}$ divided by the coupling-squared $g^2_{NP}$ of relevant new
physics.
