Using the long-range corrected spin-unrestricted density functional theory (LC-UBLYP) method, we have investigated the longitudinal third-order nonlinear optical (NLO) properties, i.e., the second hyperpolarizabilities gamma of open-shell singlet one-dimensional (ID) extended metal atom chain (EMAC) systems, chromium(II) chains Cr-2n(II) (n = 1 - 4), with different metal-metal bond lengths from the viewpoint of the open-shell character dependences of each d orbital contribution (d sigma, d pi, d delta) to gamma and of the chain-length dependence of gamma. It turns out that the chain length dependences of the open-shell characters of d pi and do orbitals at any metal-metal bond length are negligible, while the d sigma open-shell character decreases as a function of chain length. The systems display bell-shaped behaviors of gamma as a function of the metal-metal bond length, in which the gamma values attain maxima for intermediate d sigma open-shell character. The maximum gamma value (gamma(max)) exhibits remarkable enhancement as a function of chain length. It is also found that the bond length alternation (BLA) significantly affects the gamma values and their chain-length dependences. The present results provide the guiding principles for designing transition-metal complexes with open-shell singlet ID metallic chains exhibiting large third-order optical nonlinearity.