We present direct experimental observation of exciton-phonon bound states in the photoluminescence excitation spectra of isolated single walled carbon nanotubes in aqueous suspension. The photoluminescence excitation spectra from several distinct single-walled carbon nanotubes show the presence of at least one sideband related to the tangential modes, lying {200 meV} above the main absorption/emission peak. Both the energy position and line shapes of the sidebands are in excellent agreement with recent calculations [PRL {bf 94},027402 (2005)] that predict the existence of exciton-phonon bound states, a sizable spectral weight transfer to these exciton-phonon complexes and that the amount of this transfer depends on the specific nanotube structure and diameter. The observation of these novel exciton-phonon complexes is a strong indication that the optical properties of carbon nanotubes have an excitonic nature and also of the central role played by phonons in describing the excitation and recombination mechanisms in carbon nanotubes.
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