The complete crystallography of a one-dimensional crystal of potassium iodide encapsulated within a 1.6-nanometer-diameter single-walled carbon nanotube has been determined with high-resolution transmission electron microscopy. Individual atoms of potassium and iodine within the crystal were identified from a phase image that was reconstructed with a modified focal series restoration approach. The lattice spacings within the crystal are substantially different from those in bulk potassium iodide. This is attributed to the reduced coordination of the surface atoms of the crystal and the close proximity of the van der Waals surface of the confining nanotube.