  We present a definitive assessment of the role of Inverse Compton scattering
of Cosmic Microwave Background photons (IC/CMB) in the context of radio
galaxies. Owing to the steep increase of the CMB radiation energy density,
IC/CMB is supposed to become progressively more important with respect to radio
synchrotron cooling as the redshift increases. For typical energies at play,
this process will up-scatter the CMB photons into the X-ray band, and is thus
expected to yield a redshift-dependent, concurrent X-ray brightening and radio
dimming of the jet-powered structures. Here we show how a conclusive proof of
this effect hinges on high-resolution imaging data in which the extended lobes
can be distinguished from the compact hot spots where synchrotron-self-Compton
dominates the X-ray emission regardless of redshift. We analyze Chandra and
Very Large Array data of 11 radio galaxies between 1.3<z<4.3, and demonstrate
that the emission from their lobes is fully consistent with the expectations
from IC/CMB in equipartition. Once the dependence on size and radio luminosity
are properly accounted for, the measured lobe X-ray luminosities bear the
characteristic (1+z)**4 proportionality expected of a CMB seed radiation field.
Whereas this effect can effectively quench the (rest-frame) GHz radio emission
from z>3 radio galaxies below <1 mJy, IC/CMB alone can not be responsible for a
deficit in high-z, radio-loud AGN if--as we argue--such AGN typically have
bright, compact hot spots.
