We report the discovery of extended X-ray emission around the powerful high-redshift quasar GB 1508+5714 at z =4.3 , revealed in a long Chandra ACIS observation . The emission feature is 3–4 arcsec away from the quasar core , which corresponds to a projected distance of about 25 kpc . The X-ray spectrum is best fitted with a power law of photon index 1.92 \pm 0.35 ( 90 per cent c.l . ) . The X-ray flux and luminosity reach 9.2 10 ^ { -15 } { erg cm ^ { -2 } s ^ { -1 } } ( 0.5–8 keV ) and 1.6 10 ^ { 45 } { erg s ^ { -1 } } ( 2.7–42.4 keV rest frame , \Omega _ { \Lambda } =0.73 , \Omega _ { m } =0.27 , H _ { 0 } =71 km s ^ { -1 } Mpc ^ { -1 } ) , which is about 2 percent of the total X-ray emission of the quasar . We interpret the X-ray emission as inverse Compton scattering of Cosmic Microwave Background photons . The scattering relativistic electron population could either be a quasi-static diffuse cloud fed by the jet , or an outer extension of the jet with a high bulk Lorentz factor . We argue that the lack of an obvious detection of radio emission from the extended component could be a consequence of Compton losses on the electron population , or of a low magnetic field . Extended X-ray emission produced by inverse Compton scattering may be common around high redshift radio galaxies and quasars , demonstrating that significant power is injected into their surrounding by powerful jets .