We present what we believe to be the first experimental determination of the third-order optical susceptibility chi((3)) of bulk cuprous oxide (Cu(2)O) crystals. The measured nonlinear refractive index, obtained with the Z-scan technique at 1064 nm, is n(2)=1.32x10(-10) esu, while the two-photon absorption coefficient is beta=5.0 cm/GW of Cu(2)O. We also observe strong third-harmonic generation (THG) from Cu(2)O in our detection range owing to its unique crystal and electronic structure. Considering that the first nonvanishing nonlinear term is chi((3)), this classical semiconductor could be utilized as a promising active THG medium.