Spectra of the third-order nonlinear susceptibility chi((3)) have been investigated for one-dimensional Mott insulators, Sr(2)CuO(3) and Ca(2)CuO(3), by applying the third-harmonic generation (THG) spectroscopy on their single-crystalline thin films. The three-photon resonance to the lowest charge-transfer (CT) state with odd parity strongly enhances chi((3)), which is of the order of 10(-9) esu. The two-photon resonant structure unravels the even-CT state, located close to the odd-CT state. Two types of chi((3)) spectra obtained from THG and the electroreflectance measurements are explained based on the concept of spin-charge separation.