  We describe the design and performance of a large-area scintillator hodoscope
onboard the BESS rigidity spectrometer; an instrument with an acceptance of 0.3
m^{2}sr.
  The hodoscope is configured such that 10 and 12 counters are respectively
situated in upper and lower layers.
  Each counter is viewed from its ends by 2.5 inch fine-mesh photomultiplier
tubes placed in a stray magnetic field of 0.2 Tesla.
  Various beam-test data are presented.
  Use of cosmic-ray muons at ground-level confirmed 50 ps timing resolution for
each layer, giving an overall time-of-flight resolution of 70 ps rms using a
pure Gaussian resolution function.
  Comparison with previous measurements on a similar scintillator hodoscope
indicates good agreement with the scaling law that timing resolution is
proportional to 1/$\sqrt{N_{\rm pe}}$, where $N_{\rm pe}$ is the effective
number of photoelectrons.
