  This letter reports on a search for $\nu_\mu \to \nu_e$ transitions by the
MINOS experiment based on a \unit[$3.14\times10^{20}$]{protons-on-target}
exposure in the Fermilab NuMI beam. We observe 35 events in the Far Detector
with a background of $27\pm 5 {\rm (stat.)} \pm 2 {\rm (syst.)$ events
predicted by the measurements in the Near Detector. If interpreted in terms of
$\nu_\mu \to \nu_e$ oscillations, this 1.5 $\sigma$ excess of events is
consistent with $\sin^{2}(2\theta_{13})$ comparable to the CHOOZ limit when
$|\delmsq{}|$=\unit[2.43$\times 10^{-3}$] {${\rm eV^{2}}$} and \sinsq{23}=1.0
are assumed.
