The Chandra X-Ray Observatory has proved to have the unique capability to detect jets and hot spots in quasars and radio sources. If X-rays from any of the observed objects are due to inverse Compton scattering of relativistic electrons on the cosmic microwave background (CMB) radiation, then such an object will be detectable with the same surface brightness anywhere in the more distant universe. This is because the enhancement of the CMB energy density by a factor of (1+z)4 compensates for the (1+z)–4 decrease of surface brightness. These may already have been detected in X-ray surveys, and we point out the unique considerations that must be applied to correctly identify them, namely, that the jets could outshine the parent quasars, that a few arcsecond X-ray position circle will likely not include the quasar, and that the X-ray source will be resolved with telescopes that have 2" resolution. We predict that Chandra will detect many of these in the next observing cycle, for example, in a distant Sloan survey quasar or the ROSAT X-ray source PKS 2215+020.