The millimeter-wavelength hydrogen recombination lines H40?, H53?, and H66? have been observed in the nucleus of the nearby starburst galaxy NGC 253. The line fluxes have been compared with existing radio recombination line measurements and are found to be consistent with spontaneous emission from optically thin H II regions. The inferred hydrogen ionization rate is (3.7 ? 0.8) ? 1053 s-1. This value is up to an order of magnitude larger than those inferred from the recombination lines Br? and Br?, implying substantial extinction due to dust even at near-infrared wavelengths. Comparison with existing 3.3 mm continuum measurements implies an electron temperature for the gas of (5000 ? 900) K if the continuum at this wavelength is entirely due to free-free emission.