  We have obtained intermediate resolution spectra of eleven candidate brown
dwarf members of the Pleiades open cluster using the Keck II telescope and LRIS
spectrograph. Our primary goal was to determine the location of the "lithium
depletion edge" in the Pleiades and hence to derive a precise age for the
cluster. All but one of our 11 program objects have radial velocities
appropriate for Pleiades members, have moderately strong H alpha emission, and
have spectral types M6 to M8.5, as expected for their (R-I) colors.
  We have constructed a color-magnitude diagram for the faint end of the
Pleiades main sequence, including only stars for which high S/N spectra in the
region of the lithium 6708 Angstrom absorption line have been obtained. These
data allow us to accurately determine the Pleiades single-star lithium
depletion edge at I(c0) = 17.80, R-I(c0) = 2.20, spectral type = M6.5. By
reference to theoretical evolutionary models, this converts fairly directly
into an age for the Pleiades of 125 Myr. This is significantly older than the
age that is normally quoted, but does agree with some other recent estimates.
