Measurements of stepwise photoluminescence quenching in individual, (n,m)-selected single-walled carbon nanotubes (SWCNTs) undergoing chemical reaction have been analyzed to deduce mobilities of optically generated excitons. For (7,5) nanotubes, the mean exciton range varies between similar to 140 and 240 nm for different surfactant coatings and correlates weakly with nanotube PL intensity. The results are consistent with a model of localized SWCNT excitons having substantial diffusional mobility along the nanotube axis.