Noble-metal nanoparticles have had a substantial impact across a diverse range of fields, including catalysis, sensing, photochemistry, optoelectronics, energy conversion and medicine. Although silver has very desirable physical properties, good relative abundance and low cost, gold nanoparticles have been widely favoured owing to their proved stability and ease of use. Unlike gold, silver is notorious for its susceptibility to oxidation (tarnishing), which has limited the development of important silver-based nanomaterials. Despite two decades of synthetic efforts, silver nanoparticles that are inert or have long-term stability remain unrealized. Here we report a simple synthetic protocol for producing ultrastable silver nanoparticles, yielding a single-sized molecular product in very large quantities with quantitative yield and without the need for size sorting. The stability, purity and yield are substantially better than those for other metal nanoparticles, including gold, owing to an effective stabilization mechanism. The particular size and stoichiometry of the product were found to be insensitive to variations in synthesis parameters. The chemical stability and structural, electronic and optical properties can be understood using first-principles electronic structure theory based on an experimental single-crystal X-ray structure. Although several structures have been determined for protected gold nanoclusters, none has been reported so far for silver nanoparticles. The total structure of a thiolate-protected silver nanocluster reported here uncovers the unique structure of the silver thiolate protecting layer, consisting of Ag2S5 capping structures. The outstanding stability of the nanoparticle is attributed to a closed-shell 18-electron configuration with a large energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, an ultrastable 32-silver-atom excavated-dodecahedral core consisting of a hollow 12-silver-atom icosahedron encapsulated by a 20-silver-atom dodecahedron, and the choice of protective coordinating ligands. The straightforward synthesis of large quantities of pure molecular product promises to make this class of materials widely available for further research and technology development.