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 2.5sigma 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.
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