  We present and discuss the development and performance of a compact
scintillating fiber (SciFi) detector for timing to be used in the Mu3e
experiment at very high particle rates. The SciFi detector is read out with
multichannel silicon photomuiltipliers (SiPM) arrays at both ends to achieve
the best timing performance. Mu3e is a new experiment under preparation at the
Paul Scherrer Institute to search for charged Lepton Flavor Violation in the
rare neutrinoless muon decay mu->eee using the most intense continuous surface
muon beam in the world. The Mu3e detector is based on thin high-voltage
monolithic active silicon pixel sensors (HV-MAPS) for very precise tracking in
conjunction with scintillating fibers and scintillating tiles coupled to SiPMs
for accurate timing measurements and it is designed to operate at very high
intensities.
  In order to reach a single event sensitivity of 10^-16 for this rare mu->eee
muon decay, all backgrounds must be rejected well below this level. To suppress
all forms of accidental background, a very thin SciFi detector (thickness <
0.2% of a radiation length X_0) with a time resolution of 250 ps, efficiency in
excess of 96%, and spatial resolution of 100 micron has been developed. In this
paper we report on the development, construction, and performance of this SciFi
detector. Different scintillating fiber types have been evaluated and various
assembly procedures have been tested to achieve the best performance.
  The compact size, fast response, good timing, high spatial resolution,
insensitivity to magnetic fields, and adaptable geometry make SciFi detectors
suitable for a variety of applications.
