We report on the detection of a soft spatially extended component of X-ray emission around four intermediate-redshift 3C quasars observed with Chandra: 3C 254, 3C 263, 3C 275.1 and 3C 281. The bolometric luminosity of this emission ranges over 0.3-1.6 x 10(44) erg s(-1), and extends to length-scales of over 350 kpc at the redshift of the quasar. The X-rays are most likely thermal emission from the intracluster medium of a cluster of galaxies around each quasar, which provides the working surface for the powerful radio lobes. Some X-ray emission is also seen to be associated with the radio plasma.