The effect of charging on the longitudinal second hyperpolarizability of polyacetylene (PA) chains containing up to nearly 70 carbon atoms has been investigated ab initio by characterizing chains with and without an explicit alkali atom (Li, Na, K) as dopant. Whereas charging dramatically enhances the static electronic and vibrational hyperpolarizabilities, gamma(L)(e)(0) and gamma(L)(v), of an isolated chain at intermediate chain lengths, the presence of an alkali atom counterion substantially reduces this effect. As the size of the alkali atom increases, most properties, including the hyperpolarizabilities, approach those of the isolated chain. Detailed analysis shows that the behavior of gamma(L)(e)(0) is most simply explained in terms of a reduced electrostatic pinning potential due to increased distance between chain and counterion. At all chain lengths studied gamma(L)(e)(0) of PA is enhanced by alkali doping. For chains containing 50 carbon atoms (N-C=50), the increase due to K doping is about 9x10(7)a.u., which more than doubles the value for an undoped chain of similar length. The normalized quantity gamma(L)(e)(0)/N-C exhibits a maximum for the isolated soliton (at about N-C=61) that is over four times that of the infinite undoped (and unbent) chain. When the alkali dopant is taken into account this maximum diminishes considerably and shifts to larger N-C than we have considered. In comparison with the maximum for the undoped species (at N-C=infinity) there is a small enhancement of gamma(L)(e)(0)/N-C for K doping, but none for either Li or Na doping at the coupled-perturbed Hartree-Fock (CPHF)/6-31G level of theory. Intermediate length isolated chains bearing a charged soliton show order of magnitude increases in gamma(v) for the degenerate four-wave mixing (DFWM) and, especially, electric field-induced second harmonic generation (dc-SHG) processes compared to undoped PA. As in the case of gamma(L)(e)(0) this enhancement persists, but is significantly reduced when the dopant atom is included. Vibrational anharmonicity, which contributes only to the dc Kerr effect at our level of treatment, is much more important in the doped than undoped species.