Our XMM-Newton spectrum of the giant, high-redshift (z=1.88) radio galaxy 6C 0905+39 shows that it contains one of the most powerful, high-redshift, Compton-thick quasars known. Its spectrum is very hard above 2 keV. The steep XMM spectrum below that energy is shown to be due to extended emission from the radio bridge using Chandra data. The nucleus of 6C 0905+39 has a column density of 3.5 (+1.4,-0.4) X 10^24 cm^-2 and absorption-corrected X-ray luminosity of 1.7 (+0.9,-0.1) X 10^45 erg/s in the 2-10 keV band. A lower redshift active galaxy in the same field, SDSS J090808.36+394313.6, may also be Compton-thick.