We theoretically investigate the open-shell singlet nature and sigma-/pi-conjugation effects on the longitudinal second hyperpolarizabilities (gamma) of one-dimensional chains involving silicon silicon bonds, that is, polysilane and poly(disilene-1,2-diyl), by comparison with their carbon analogues, polyethylene and polyacetylene, respectively. It is found that poly(disilene-1,2-diyl) has less bond length alternation than polyacetylene and that sigma-conjugation of polysilane is less effective on the enhancement of gamma than pi-conjugation of polyacetylene, whereas pi-conjugation of poly(disilene-1,2-diyl) indicates a more than 20 times greater enhancement of the gamma than that of polyacetylene, which is known to be a typical nonlinear optical molecule with large gamma, for one-dimensional chains involving 3-5 double bonds. Further theoretical analyses of poly(disilene-1,2-diyl) reveal the sigma- and pi-electrons contribute negatively and positively to the gamma, respectively. The latter contribution is significantly larger than the former and thus causes the remarkable enhancement of gamma amplitudes due to the emerging open-shell singlet nature in the long,pi-conjugation length.