We present and discuss the results of a numerical investigation on the susceptivity for third-harmonic generation in mixed valent ruthenium-pyrazine chains (which we may call ''Creutz-Taube chains''), whose skeleton is made by ruthenium ions bridged by pyrazine ligands. These compounds are described by a two-band Hubbard Hamiltonian, which, according to our previous results, is capable of reproducing the main features of the optical spectra in the near-IR-vis as a function of the total charge of the ion (i.e., the number of Ru2+ and Ru3+ ions). The third-harmonic susceptivity, computed exactly through a linear algebraic method (avoiding the sum over states) is remarkably high, suggesting that these compounds may be good candidates for nonlinear optics and photonics.