We investigated the X-ray emission properties of the powerful radio galaxy 3C 459 revealed by a recent Chandra follow-up observation carried out in October 2014 with a 62 ks exposure. We performed an X-ray spectral analysis from a few selected regions on an image obtained from this observation and also compared the X-ray image with a 4.9 GHz VLA radio map available in the literature. The dominant contribution comes from the radio core but significant X-ray emission is detected at larger angular separations from it, surrounding both radio jets and lobes. According to a scenario in which the extended X-ray emission is due to a plasma collisionally heated by jet-driven shocks and not magnetically dominated, we estimated its temperature to be ~0.8 keV. This hot gas cocoon could be responsible for the radio depolarization observed in 3C 459, as recently proposed also for 3C 171 and 3C 305. On the other hand, our spectral analysis and the presence of an oxygen K edge, blueshifted at 1.23 keV, cannot exclude the possibility that the X-ray radiation originating from the inner regions of the radio galaxy could be intercepted by some outflow of absorbing material intervening along the line of sight, as already found in some BAL quasars.