  We propose an experiment (Mu3e) to search for the lepton flavour violating
decay mu+ -> e+e-e+. We aim for an ultimate sensitivity of one in 10^16
mu-decays, four orders of magnitude better than previous searches. This
sensitivity is made possible by exploiting modern silicon pixel detectors
providing high spatial resolution and hodoscopes using scintillating fibres and
tiles providing precise timing information at high particle rates.
