We present high-resolution X-ray observations of the narrow-line radio galaxy PKS 1138-262 at z = 2.156 with the ACIS-S detector on the Chandra X-Ray Observatory . These observations show that the X-ray emission from 1138-262 is dominated by emission from the active galactic nucleus (AGN) with a 2-10 keV luminosity of 4 × 10 45 ergs s -1 . The relative X-ray and radio properties of the AGN in 1138-262 are similar to those seen for the AGN in the archetype powerful radio galaxy Cygnus A. Between 10% and 25% (depending on energy) of the X-ray emission from 1138-262 is spatially extended on scales of 10''-20''. The extended X-ray emission is elongated, with a major axis aligned with that of the radio source. While the X-ray and radio emissions are elongated on similar scales and position angles, there is no one-to-one correspondence between the radio and X-ray features in the source. The most likely origin for the extended X-ray emission in 1138-262 is thermal emission from shocked gas, although we cannot rule out a contribution from inverse Compton emission. If the emission is from hot gas, then the gas density is 0.05 cm -3 and the gas mass is 2.5 × 10 12 M ☉ . The pressure in this hot gas is adequate to confine the radio-emitting plasma and the optical line-emitting gas. We set an upper limit of 1.5 × 10 44 ergs s -1 to the (rest frame) 2-10 keV luminosity of any normal cluster atmosphere associated with 1138-262. No emission was detected from any of the Lyα-emitting galaxies in the (proto-) cluster around 1138-262, outside of the Lyα halo of 1138-262 itself, to a (rest frame) 2-10 keV luminosity limit of 1.2 × 10 43 ergs s -1 . Emission was detected from a z = 2.183 QSO located 2' west of 1138-262 with a luminosity of 1.8 × 10 44 ergs s -1 .
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