Glasses are generally prepared by cooling from the liquid phase, and their properties depend on their thermal history. Recent experiments indicate that glasses prepared by vapour deposition onto a substrate can exhibit remarkable stability, and might correspond to equilibrium states that could hitherto be reached only by glasses aged for thousands of years. Here we create ultrastable glasses by means of a computer-simulation process that mimics physical vapour deposition. These stable glasses have, far below the conventional glass-transition temperature, the properties expected for the equilibrium supercooled liquid state, and optimal stability is attained when deposition occurs at the Kauzmann temperature. We also show that the glasses' extraordinary stability is associated with distinct structural motifs, in particular the abundance of regular Voronoi polyhedra and the relative lack of irregular polyhedra.