  We report the discovery in an 80-ks observation of spatially-extended X-ray
emission around the high-redshift radio galaxy TNJ1388-1942 (z=4.11) with the
Chandra X-ray Observatory. The X-ray emission extends over a ~30-kpc diameter
region and although it is less extended than the GHz-radio lobes, it is roughly
aligned with them. We suggest that the X-ray emission arises from Inverse
Compton (IC) scattering of photons by relativistic electrons around the radio
galaxy. At z=4.11 this is the highest redshift detection of IC emission around
a radio galaxy. We investigate the hypothesis that in this compact source, the
Cosmic Microwave Background (CMB), which is ~700x more intense than at z~0 is
nonetheless not the relevant seed photon field for the bulk of the IC emission.
Instead, we find a tentative correlation between the IC emission and
far-infrared luminosities of compact, far-infrared luminous high-redshift radio
galaxies (those with lobe lengths of <100kpc). Based on these results we
suggest that in the earliest phases of the evolution of radio-loud AGN at very
high redshift, the far-infrared photons from the co-eval dusty starbursts
occuring within these systems may make a significant contribution to their IC
X-ray emission and so contribute to the feedback in these massive high-redshift
galaxies.
