Strong quantum confinement and low dielectric screening impart single-walled carbon nanotubes with exciton-binding energies substantially exceeding kBT at room temperature. Despite these large binding energies, reported photoluminescence quantum yields are typically low and some studies suggest that photoexcitation of carbon nanotube excitonic transitions can produce free charge carriers. Here we report the direct measurement of long-lived free-carrier generation in chirality-pure, single-walled carbon nanotubes in a low dielectric solvent. Time-resolved microwave conductivity enables contactless and quantitative measurement of the real and imaginary photoconductance of individually suspended nanotubes. The conditions of the microwave conductivity measurement allow us to avoid the complications of most previous measurements of nanotube free-carrier generation, including tube-tube/tube-electrode contact, dielectric screening by nearby excitons and many-body interactions. Even at low photon fluence (approximately 0.05 excitons per μm length of tubes), we directly observe free carriers on excitation of the first and second carbon nanotube exciton transitions.