Single-molecule chemical reactions with individual single-walled carbon nanotubes were observed through near-infrared photoluminescence microscopy. The emission intensity within distinct submicrometer segments of single nanotubes changed in discrete steps after exposure to acid, base, or diazonium reactants. The steps were uncorrelated in space and time and reflected the quenching of mobile excitons at localized sites of reversible or irreversible chemical attack. Analysis of step amplitudes revealed an exciton diffusional range of about 90 nanometers, independent of nanotube structure. Each exciton visited about 10,000 atomic sites during its lifetime, providing highly efficient sensing of local chemical and physical perturbations.