  (Abridged) We present deep Keck spectroscopy, using the DEIMOS and LRIS
spectrographs, of a large and representative sample of 67 ``Extremely Red
Objects'' (EROs) to H=20.5, with I-H>3.0, in three of the Las Campanas Infrared
Survey fields. Spectroscopic redshifts are determined for 44 sources, of which
only two are contaminating low mass stars. When allowance is made for
incompleteness, the spectroscopic redshift distribution closely matches that
predicted earlier on the basis of photometric data. Our spectra are of
sufficient quality that we can address the important question of the nature and
homogeneity of the z>0.8 ERO population. A dominant old stellar population is
inferred for 75% of our spectroscopic sample; a higher fraction than that seen
in smaller, less-complete samples with broader photometric selection criteria
(e.g. R-K). However, only 28% have spectra with no evidence of recent star
formation activity, such as would be expected for a strictly passively-evolving
population. More than ~30% of our absorption line spectra are of the `E+A' type
with prominent Balmer absorption consistent, on average, with mass growth of
5-15% in the past Gyr. We use our spectroscopic redshifts to improve earlier
estimates of the spatial clustering of this population as well as to understand
the significant field-to-field variation. Our spectroscopy enables us to
pinpoint a filamentary structure at z=1.22 in the Chandra Deep Field South.
Overall, our study suggests that the bulk of the ERO population is an
established population of clustered massive galaxies undergoing intermittent
activity consistent with continued growth over the redshift interval 0.8<z<1.6.
