Three-photon absorption of a series of donor-acceptor trans-stilbene derivatives is studied by means of density functional theory applied to the third-order response function and its residues. The results obtained by using different functionals are compared with experimental data for similar systems obtained from the literature. With a Coulomb attenuated, asymptotically corrected functional, the excitation energy to the first resonance state is much improved. Comparison with experiment indicates that this is the case for the three-photon cross section as well. In particular, the overestimation of the cross sections and underestimation of excitation energies offered by the density functional theory using common density functionals is corrected for. It is argued that a reliable theory for three-photon absorption in charge transfer and other chromophore systems thereby has been obtained. Further elaboration of the theory and its experimental comparison call for explicit inclusion of solvent polarization and pulse propagation effects.