We have generated and detected the radial-breathing mode of coherent lattice vibrations in single-walled carbon nanotubes using ultrashort laser pulses. Because the band gap is a function of diameter, these diameter oscillations cause ultrafast band gap oscillations, modulating interband excitonic resonances at the phonon frequencies (3-9 THz). Excitation spectra show a large number of pronounced peaks, mapping out chirality distributions in great detail.