The quasar PKS 0637-752, the first celestial X-ray target of the Chandra X-
Ray Observatory, has revealed asymmetric X-ray structure extending from 3"
to 12" west of the quasar, coincident with the inner portion of the jet pre
viously detected in a 4.8 GHz radio image (Tingay et al. 1998). At a redshi
ft of z = 0.651, the jet is the largest (greater than or similar to 100 kpc
in the plane of the sky) and most luminous (similar to 10(44.6) ergs s(-1)
) of the few so far detected in X-rays. This Letter presents a high-resolut
ion X-ray image of the jet, from 42 ks of data when PKS 0637-752 was on-axi
s 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 Australian Telescope
Compact Array radio images at 4.8 and 8.6 GHz. Observations of the parsec-
scale core using the very long baseline interferometry space observatory pr
ogram mission show structure aligned with the X-ray jet, placing important
constraints on the X-ray source models. Hubble Space Telescope images show
that there are three small knots coincident with the peak radio and X-ray e
mission. Two of these are resolved, which we use to estimate the sizes of t
he X-ray and radio knots. The outer portion of the radio jet and a radio co
mponent to the east show no X-ray emission to a limit of about 100 times Lo
wer flux. The X-ray emission is difficult to explain with models that succe
ssfully account for extranuclear X-ray/radio structures in other active gal
axies. We think the most plausible is a synchrotron self-Compton model, but
this would imply extreme departures from the conventional minimum energy a
nd/or homogeneity assumptions. We also rule out synchrotron or thermal brem
sstrahlung models for the jet X-rays, unless multicomponent or ad hoc geome
tries are invoked.