We have observed the C91alpha radio recombination line toward the Orion H II region. This narrow (approximately 3-5 km s-1 FWHM) line is spatially very extended (approximately 8' or 1 pc). These characteristics compare well with the observed characteristics of the C II fine structure line at 158 mum. Thus, the C91alpha line originates in the predominantly neutral photodissociation regions separating the H II region from the molecular cloud. We have developed theoretical models for the C ii radio recombination lines from photodissociation regions. The results show that the I(C91alpha)/I(C158) intensity ratio is a sensitive function of the temperature and density of the emitting gas. We have also extended existing theoretical models for photodissociation regions to include the C II recombination lines. Comparison with these models show that, in the central portion of the Orion region, the C91alpha line originates in dense (10(6) cm-3), warm (500-1000 K) gas. Even at large projected distances (approximately 1 pc), the inferred density is still high (10(5) cm-3) and implies extremely high thermal pressures. As in the case of the [C II] 158 mum line, the large extent of the C91alpha line shows that FUV photons can penetrate to large distances from the illuminating source. The decline of the intensity of the incident radiation field with distance from THETA1 C seems to be dominated by geometrical dilution, rather than dust extinction. Finally, we have used our models to calculate the intensity of the 9850 angstrom recombination line of C II. The physical conditions inferred from this line are in good agreement with those determined from the radio recombination and the far-infrared fine-structure lines. We show that the ratio of the 9850 angstrom to the C91alpha line is a very good probe of very high density clumps.