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 changes in discrete steps after exposure to acid, base, or diazonium reactants. The steps are uncorrelated in space and time, and reflect the quenching of mobile excitons at localized sites of reversible or irreversible chemical attack. Analysis of step amplitudes reveals an exciton diffusional range of about 90 nanometers, independent of nanotube structure. Each exciton visits approximately 104 atomic sites during its lifetime, providing highly efficient sensing of local chemical and physical perturbations.