We have discovered an X-ray jet with Chandra imaging of the z =1.187 radio-loud quasar PKSÂ 1127-145 . In this paper we present the Chandra X-ray data , follow-up VLA observations , and optical imaging using the HST WFPC2 . The X-ray jet contains 273 \pm 5 net counts in 27 ksec and extends \sim 30 \arcsec from the quasar core , corresponding to a minimum projected linear size of \sim 330 h _ { 50 } ^ { -1 } Â kpc . The evaluation of the X-ray emission processes is complicated by the observed offsets between X-ray and radio brightness peaks . We discuss the problems posed by these observations to jet models . In addition , PKS 1127-145 is a Giga-Hertz Peaked Spectrum radio source , a member of the class of radio sources suspected to be young or “ frustrated ” versions of FRI radio galaxies . However the discovery of an X-ray and radio jet extending well outside the host galaxy of PKS 1127-145 suggests that activity in this and other GPS sources may be long-lived and complex .