We report the detection at X-rays of the radio/optical hotspot and knots of 3C 303 from a short ( 15 ksec ) Chandra exposure in 2001 March . The X-ray morphology is similar to that of the radio/optical emission with peaks in the X-ray emission found at 5.5 ^ { \prime \prime } ( knot B ) , 9 ^ { \prime \prime } ( knot C ) and 17 ^ { \prime \prime } ( hotspot ) from the core of 3C 303 . Despite the limited signal-to-noise ratio of the short Chandra exposure , the X-ray photon spectrum was measured for the hotspot . We construct the spectral energy distribution ( SED ) and find that the X-ray flux is well below the extrapolation of the radio-to-optical continuum , which we interpret as resulting from the production of X-rays via inverse Compton scattering of both synchrotron photons ( SSC ) and cosmic microwave background photons ( EC/CMB ) . The magnetic field strength , region size , and the maximum energy of electrons are self-consistently determined for the hotspot to be B \simeq 4.3 \mu G , R \simeq 6.5 \times 10 ^ { 21 } cm , and \gamma _ { max } \simeq 1.4 \times 10 ^ { 7 } . This implies a magnetic field strength a factor of \sim 30 below the equipartition value ; B _ { eq } \simeq 150 \mu G. The origin of this large departure from equipartition is still uncertain , but the discrepancy is reduced if the plasma in the hotspot is moving with mildly relativistic speeds . Our observation of 3C 303 , as well as recent Chandra detections of large scale jets and hotspots in a number of radio galaxies , confirm that particles are accelerated very efficiently in radio galaxies .