  We present the results of Chandra observations of the Cl1604 supercluster at
z~0.9. The system is the largest structure mapped at redshifts approaching
unity, containing at least eight spectroscopically confirmed galaxy clusters
and groups. Using two 50-ksec ACIS-I pointings we examine both the X-ray point
source population and the diffuse emission from individual clusters in the
system. We find a 2.5\sigma excess of point sources detected in the hard band
(2-10 keV) relative to the number of sources found in blank fields observed by
Chandra. No such excess is observed in the soft band (0.5-2 keV). The hard-band
source density is 1.47 times greater than that of a blank field, in agreement
with the previously reported correlation between overdensity amplitude and
cluster redshift. Using a maximum likelihood technique we have matched 112 of
the 161 detected X-ray point sources to optical counterparts and found 15
sources that are associated with the supercluster. All 15 sources have
rest-frame luminosities consistent with emission from active galactic nuclei
(AGN). We find that the supercluster AGN largely avoid the densest regions of
the system and are instead distributed on the outskirts of massive clusters or
within poorer clusters and groups. We have also detected diffuse emission from
two of the eight clusters and groups in the system, clusters Cl1604+4304 and
Cl1604+4314. The systems have bolometric luminosities of 1.43x10^44 and
8.20x10^43 h70^-2 erg s^-1 and gas temperatures of 3.50 (+1.82-1.08) and 1.64
(+0.65-0.45) keV, respectively. Using updated velocity dispersions, we compare
the properties of these systems to the cluster scaling relations followed by
other X-ray and optically selected galaxy clusters at high redshift.
