The exciton binding energy serves as a critical criterion for identification of the nature of elementary excitations (neutral excitons versus a pair of charged carriers) in semiconductor materials. An exciton binding energy of 0.41 eV is determined experimentally for a selected nanotube type, the (8,3) tube, confirming the excitonic nature of the elementary excitations. This determination is made from the energy difference between an electron-hole continuum and its precursor exciton. The electron-hole continuum results from dissociation of excitons following extremely rapid exciton-exciton annihilation and possibly also ultrafast relaxation from the second to the first exciton states and is characterized by distinct spectroscopic and dynamic signatures.