Abstract This paper studied the faint, diffuse extended X-ray emission associated with the radio lobes and the hot gas in the intracluster medium (ICM) environment for a sample of radio galaxies. We used shallow (∼10 ks) archival Chandra observations for 60 radio galaxies (7 FR I and 53 FR II) with 0.0222 ≤ z ≤ 1.785 selected from the 298 extragalactic radio sources identified in the 3CR catalog. We used Bayesian statistics to look for any asymmetry in the extended X-ray emission between regions that contain the radio lobes and regions that contain the hot gas in the ICM. In the Chandra broad band (0.5–7.0 keV), which has the highest detected X-ray flux and the highest signal-to-noise ratio, we found that the nonthermal X-ray emission from the radio lobes dominates the thermal X-ray emission from the environment for ∼77% of the sources in our sample. We also found that the relative amount of on-jet axis nonthermal emission from the radio lobes tends to increase with redshift compared to the off-jet axis thermal emission from the environment. This suggests that the dominant X-ray mechanism for the nonthermal X-ray emission in the radio lobes is due to the inverse Compton upscattering of cosmic microwave background (CMB) seed photons by relativistic electrons in the radio lobes, a process for which the observed flux is roughly redshift independent due to the increasing CMB energy density with increasing redshift.