Natural porous solids such as zeolites are invariably formed with inorganic cations such as Na(+) and K(+) (refs 1, 2). However, current research on new porous materials is mainly focused on the use of organic species as either structure-directing or structure-building units; purely inorganic systems have received relatively little attention in exploratory synthetic work. Here we report the synthesis of a series of three-dimensional sulphides and selenides containing highly mobile alkali metal cations as charge-balancing extra-framework cations. Such crystalline inorganic chalcogenides integrate zeolite-like architecture with high anionic framework polarizability and high concentrations of mobile cations. Such structural features are particularly desirable for the development of fast-ion conductors. These materials demonstrate high ionic conductivity (up to 1.8 x 10(-2) ohm(-1) cm(-1)) at room temperature and moderate to high humidity. This synthetic methodology, together with novel structural, physical and chemical properties, may lead to the development of new microporous and open-framework materials with potential applications in areas such as batteries, fuel cells, electrochemical sensors and photocatalysis.