  Very deep near-infrared observations have recently uncovered a significant
population of red galaxies at redshifts z>2. These distant red galaxies (DRGs)
are efficiently selected by the criterion J-K>2.3. We use Chandra data to
examine the X-ray emission from DRGs in the 5'x5' FIRES MS1054-03 field. Two of
40 DRGs with K<22 are detected by Chandra, and we infer that ~5 % of DRGs host
active nuclei with L>1.2x10^43 ergs/s. This fraction is smaller than that
inferred from optical and near-IR spectroscopy, probably largely due to strong
spectroscopic selection biases. By stacking all undetected DRGs we find that
their average X-ray flux in the 0.5-8 keV band is ~4.6x10^-17 ergs/s/cm^2. The
detection is only significant in the soft and full energy bands. The mean
detection may result from star formation, the presence of low luminosity AGN,
or a combination of both. Assuming the detection is due exclusively to star
formation, we find an average instantaneous star formation rate of 214 +- 68
(random) +- 73 (systematic) solar masses per year, in excellent agreement with
previous results from spectral energy distribution fitting when constant star
formation histories are assumed. These results may imply that DRGs contribute
significantly to the cosmic star formation rate at z~2.5. However, the mean
X-ray flux strictly provides only an upper limit to the star formation rate due
to the uncertain contribution of low luminosity, possibly obscured AGNs.
Observations at other wavelengths are needed to provide independent estimates
of the star formation rate of DRGs.
