  The multi-wavelength properties of Very Red Objects (VROs; I-K>=4) are
largely unknown as many of these sources are optically faint (I>=24) and
undetected at most wavelengths. Here we provide constraints on the X-ray
properties of VROs using the 1 Ms Chandra exposure of an 8.4'x8.4' region
within the Hawaii Flanking-Field area containing the HDF-N. We find that VROs
detected in the hard band (2-8 keV) have flat X-ray spectral slopes (Gamma ~
0.9) and X-ray properties consistent with those expected from luminous obscured
AGN. The fraction of such sources in the K<=20.1 VRO population is ~14%.
Conversely, the average X-ray spectral slope of VROs detected in the soft band
(0.5-2 keV) but not in the hard band is comparatively steep (Gamma>1.4), and
the X-ray emission from these sources is consistent with that expected from
less energetic processes (i.e., star formation, low-luminosity AGN activity,
normal elliptical galaxy emission); star-formation and low-luminosity AGN
activity scenarios are favored in those sources with irregular optical
morphologies. Stacking analyses of the X-ray emission from VROs not
individually detected at X-ray energies yield significant detections (>=99%
confidence) in the soft band and the full band (0.5-8 keV). We find this X-ray
emission is produced predominantly by the optically brightest VROs. The
simplest explanation of this result is that we have detected the average X-ray
emission from non-active VROs with low X-ray-to-optical flux ratios [log(FX/FI)
~ -2]; this is consistent with that expected if the majority of these VROs are
~ M* elliptical galaxies. A number of VROs are also detected with mid-IR (15um)
and radio emission, and we provide constraints on the nature of this emission.
