We propose that the X-ray emission detected by Chandra from the 100-kiloparsec-scale jet of PKS 0637–752 is produced through inverse Compton scattering of the Cosmic Microwave Background ( CMB ) . We analyze the physical state of the jet and show that inverse Compton scattering from the CMB is consistent with equipartition for a moderate beaming of the emission , with Doppler factor \delta \sim 10 . The power transported by the jet is then similar to that of other powerful blazars , L _ { j } \sim 10 ^ { 48 } erg s ^ { -1 } , and the jet has low radiative efficiency . The radiative cooling times of the electrons are a few thousand years , compatible with the size of the knot . The low-energy cutoff of the electron distribution is constrained to be \gamma _ { min } \sim 10 , the first such constraint from spectral considerations . A parallel analysis for the SSC model yields far less reasonable physical conditions .