The properties of two-dimensional arrays of micrometre-sized particles are of interest in relation to a wide range of phenomena, including self-organization and phase behaviour in colloid science and condensed-matter physics(1-3), the behaviour of dusty plasmas(4) and the templating of ordered structures for photonic applications(5). Most studies have used pre-existing particles such as monodisperse latex spheres, which may be manipulated with electric or magnetic fields. In contrast, we report here an inorganic solution that spontaneously precipitates a self-organized two-dimensional colloid crystal at the air/water interface. A solution of calcium hydroxide exposed to air reacts with dissolved carbon dioxide to precipitate microcrystals of calcium carbonate in the form of calcite. These aggregate at the surface to form a disordered gel mat with fractal characteristics(6). We find, however, that in aged solutions a second population of charged microcrystals with the ＇dogtooth spar＇ morphology appears on the surface. These crystallites, which can be observed by optical microscopy, become organized into a regular triangular lattice. The competition between electrostatic and capillary forces between particles leads to lattice spacings of the order of 125 to 175 mu m, 5 to 7 times the diameter of the particles. These structures are stable for around 24 h, but eventually aggregate with the fractal gel. The mechanism of their self-organization, as yet incompletely understood, might provide some insights into similar phenomena in colloid science(2,3,7-9).