An unprecedented 3-D SHG-active metal-organic framework (MOF) of silver(I), Ag-Amidn (1) (HAmidn: 2-amino-4,5-imidazoledicarbonitrile), has been successfully prepared by employing the new single ligand. The cooperative coordination of the imidazole and carbonitrile N atoms leads to the chiral triple helices accounting for the noncentrosymmetric space group, which are linked together to form a rare 10(3) topological structure. Ag-Amidn (1) with high thermal stability and insolubility may be considered as a potential second-order NLO material.