Several kiloparsec-scale X-ray jets have now been discovered with the Chandra X-ray Observatory, extending up to ~50 kpc (projected distance) from the active galactic nucleus in which the jet originates. In all cases, these jets also emit radio and optical light, which can be well explained as synchrotron radiation. We suggest that in at least some jets, including those in the Chandra ``first light'' quasar PKS 0637-752 and in the well-known quasar 3C 273, the X-rays may be produced by relativistic electrons in the jet Compton up-scattering cosmic microwave background photons. The local CMB energy density is high enough if (and only if) the jet continues to flow at nearly the speed of light many thousands of light years from the active nucleus - out to more than a million light years in the case of PKS 0637-752. The magnetic field in the jet can then be in equipartition with the electrons, the implied Doppler beaming factors agree with estimates from superluminal motion measured on smaller (parsec) scales, and the synchrotron cooling times are long enough that the de-projected jet length can be explained without any need for particle reacceleration.