The quasar PKS 0637-753, the first celestial X-ray target of the Chandra X-ray Observatory, has revealed asymmetric X-ray structure extending from 3 to 12 arcsec west of the quasar, coincident with the inner portion of the jet previously detected in a 4.8 GHz radio image (Tingay et al. 1998). At a redshift of z=0.651, the jet is the largest (~100 kpc) and most luminous (~10^{44.6} ergs/s) of the few so far detected in X-rays. This letter presents a high resolution X-ray image of the jet, from 42 ks of data when PKS 0637-753 was on-axis and ACIS-S was near the optimum focus. For the inner portion of the radio jet, the X-ray morphology closely matches that of new ATCA radio images at 4.8 and 8.6 GHz. Observations of the parsec scale core using the VSOP space VLBI mission show structure aligned with the X-ray jet, placing important constraints on the X-ray source models. HST images show that there are three small knots coincident with the peak radio and X-ray emission. Two of these are resolved, which we use to estimate the sizes of the X-ray and radio knots. The outer portion of the radio jet, and a radio component to the east, show no X-ray emission to a limit of about 100 times lower flux. The X-ray emission is difficult to explain with models that successfully account for extra-nuclear X-ray/radio structures in other active galaxies. We think the most plausible is a synchrotron self-Compton (SSC) model, but this would imply extreme departures from the conventional minimum-energy and/or homogeneity assumptions. We also rule out synchrotron or thermal bremsstrahlung models for the jet X-rays, unless multicomponent or ad hoc geometries are invoked.
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