Observations at high spectral resolution of the Br gamma hydrogen recombination line are presented for the central 25 arcsec of the starburst galaxy NGC 253. The rotation curve derived from these data shows solid body rotation consistent with recent interferometric CO measurements but not with rotation curves derived from optical emission lines. This discrepancy is most likely due to heavy dust extinction along the line of sight causing the optical lines to underestimate the radial velocity. This dust must be located foreground to the region undergoing solid body rotation.