We analyze a 100 ks Chandra observation of the powerful radio galaxy, 4C 60.07 at z = 3.79. We identify extended X-ray emission with L X ~ 1045 erg s–1 across a ~90 kpc region around the radio galaxy. The energetics of this X-ray halo and its morphological similarity to the radio emission from the galaxy suggest that it arises from inverse Compton (IC) scattering, by relativistic electrons in the radio jets, of cosmic microwave background photons and potentially far-infrared photons from the dusty starbursts around this galaxy. The X-ray emission has a similar extent and morphology to the Lyα halo around the galaxy, suggesting that it may be ionizing this halo. Indeed, we find that the GHz-radio and X-ray and Lyα luminosities of the halo around 4C 60.07 are identical to those of 4C 41.17 (also at z = 3.8) implying that these three components are linked by a single physical process. This is only the second example of highly extended IC emission known at z>3, but it underlines the potential importance of IC emission in the formation of the most massive galaxies at high redshifts. In addition, we detect two X-ray luminous active galactic nuclei (AGNs) within ~30 kpc of the radio galaxy. These two companion AGNs imply that the radio and starburst activity in the radio galaxy is triggered through multiple mergers of massive progenitors on a short timescale, 100 Myr. These discoveries demonstrate the wealth of information which sensitive X-ray observations can yield into the formation of massive galaxies at high redshifts.