We present results from a 49.4 ks Chandra /ACIS-S observation of the nearby ( z =0.059 ) X-shaped FRII radio galaxy 3C 403 . This is the first Chandra observation of an X-shaped radio galaxy , and one of the goals of this pioneering study is to determine the relationship between the X-ray emitting gas and the X-shaped radio morphology . We find that the X-ray isophotes of the hot gas within \sim 3.5 ^ { \prime \prime } of the central galaxy are highly elliptical ( eccentricity \sim 0.57 ) and co-aligned with the elliptical optical isophotes . This supports the hypothesis that X-shaped radio sources are created by propagation of jets through asymmetric density distributions . Within large uncertainties , there is no evidence that the lobes or wings are overpressurized relative to the ISM , supporting the scenario in which the wings are the result of strong backflow of material from the jet head and subsequent buoyant evolution . We have detected X-ray emission from several of the radio knots to the E of the active nucleus , and diffuse emission from the radio lobe to the W. The X-ray emission from the eastern knots can not be explained by an inverse Compton model unless they are far from equipartition . Using archival HST data , optical emission is detected from two knots , and the radio/optical/X-ray spectra are well fitted by simple synchrotron models . This is one of the strongest examples to date of X-ray synchrotron emission from multiple knots in the jet of an FR II radio galaxy . X-ray emission is also detected from the radio wings at a flux consistent with inverse Compton scattering of CMB photons from relativistic electrons if the wings are near equipartition . The nuclear spectrum is well described by a multi-component model that includes a heavily absorbed power law ( N _ { H } \sim 4 \times 10 ^ { 23 } cm ^ { -2 } ) and a bright ( EW \sim 244 eV ) , broadened Fe line . A second , less absorbed , power-law component , likely to represent unresolved emission from a pc-scale jet , is also required .