In this Letter, we report a Chandra X-ray detection of the double northern
hot spot of the radio quasar 3C 351. The hot spot has also been observed in
the optical with the Hubble Space Telescope (R band) and with the 3.5 m Te
lescopio Nazionale Galileo (B band). The radio-to-optical and X-ray spectra
are interpreted as the results of the synchrotron and synchrotron self-Com
pton mechanisms, respectively, with hot spot magnetic field strengths simil
ar to3 times smaller than the equipartition values. In the framework of sho
ck acceleration theory, we show that the requirement for such a relatively
small field strength is in agreement with the fitted synchrotron spectral m
odels and with the sizes of the hot spots. Finally, we show that the combin
ation of a lower magnetic field strength with the high frequencies of the s
ynchrotron cutoff in the fitted synchrotron spectra provides strong evidenc
e for electron acceleration in the hot spots.