We measured third-order nonlinear susceptibility (chi(3)) spectra in semiconducting single-walled carbon nanotubes (SWNTs) by the Z-scan method. |Imchi(3)| is remarkably enhanced under resonant excitation to the lowest interband transition, reaching 4.2 x 10(-6) esu and 1.5 x 10(-7) esu in SWNTs grown by the laser ablation and HiPco methods, respectively. A comparison of the transient absorption changes evaluated by degenerate and nondegenerate pump-probe measurements suggests that the resonant enhancement of |Imchi(3)| is dominated by a coherent process rather than by saturation of absorption.