  Merger simulations predict that tidally induced gas inflows can trigger
kpc-scale dual active galactic nuclei (dAGN) in heavily obscured environments.
Previously with the Very Large Array, we have confirmed four dAGN with
redshifts between $0.04 < z < 0.22$ and projected separations between 4.3 and
9.2 kpc in the SDSS Stripe 82 field. Here, we present $Chandra$ X-ray
observations that spatially resolve these dAGN and compare their
multi-wavelength properties to those of single AGN from the literature. We
detect X-ray emission from six of the individual merger components and obtain
upper limits for the remaining two. Combined with previous radio and optical
observations, we find that our dAGN have properties similar to nearby
low-luminosity AGN, and they agree well with the black hole fundamental plane
relation. There are three AGN-dominated X-ray sources, whose X-ray
hardness-ratio derived column densities show that two are unobscured and one is
obscured. The low obscured fraction suggests these dAGN are no more obscured
than single AGN, in contrast to the predictions from simulations. These three
sources show an apparent X-ray deficit compared to their mid-infrared continuum
and optical [OIII] line luminosities, suggesting higher levels of obscuration,
in tension with the hardness-ratio derived column densities. Enhanced
mid-infrared and [OIII] luminosities from star formation may explain this
deficit. There is ambiguity in the level of obscuration for the remaining five
components since their hardness ratios may be affected by non-nuclear X-ray
emissions, or are undetected altogether. They require further observations to
be fully characterized.
