Using the spin-unrestricted density functional theory method, we investigate the relationship between structure, spin state, and second hyperpolarizability (γ) of the finite and infinite one-dimensional open-shell aggregates composed of cyclic thiazyl radicals, that is, 1,2,3,5-dithiadiazolyl (DTDA) radicals. The DTDA aggregates with antiferromagnetic spin-alignment exhibit much greater enhancement of γ than the aggregates with ferromagnetic spin-alignment and the closed-shell benzene aggregates due to the intermediate open-shell singlet nature of the antiferromagnetic DTDA aggregate. It is found that this enhancement shows strong intermolecular distance dependences: the intermolecular distance giving the largest enhancement of γ decreases with increasing the number of molecules, and intermolecular distance alternation reduces the γ. For the infinite antiferromagnetic DTDA aggregate with a realistic intermolecular distance d = 3.1 Å, the γ per monomer reaches 1.9 × 106 au, which is comparable to that of the infinite open-shell singlet aggregate of phenalenyl radicals, and exhibits ∼2400 times enhancement as compared to that of the closed-shell benzene aggregate. This feature indicates the high-potential application of open-shell singlet cyclic thiazyl radical aggregates to outstanding third-order NLO materials.