The separation of molecules with similar size and shape is an important technological challenge. For example, rare gases can pose either an economic opportunity or an environmental hazard and there is a need to separate these spherical molecules selectively at low concentrations in air. Likewise, chiral molecules are important building blocks for pharmaceuticals, but chiral enantiomers, by definition, have identical size and shape, and their separation can be challenging. Here we show that a porous organic cage molecule has unprecedented performance in the solid state for the separation of rare gases, such as krypton and xenon. The selectivity arises from a precise size match between the rare gas and the organic cage cavity, as predicted by molecular simulations. Breakthrough experiments demonstrate real practical potential for the separation of krypton, xenon and radon from air at concentrations of only a few parts per million. We also demonstrate selective binding of chiral organic molecules such as 1-phenylethanol, suggesting applications in enantioselective separation.