Differential cross sections for the reaction gamma p --> eta' p have been measured with the CLAS spectrometer and a tagged photon beam with energies from 1.527 to 2.227 GeV. The results reported here possess much greater accuracy than previous measurements. Analyses of these data suggest for the first time the coupling of the eta'N channel to both the S11(1535) and P11(1710) resonances, known to couple strongly to the etaN channel in photoproduction on the proton, and the importance of J = 3/2 resonances in the process.