THE spontaneous breaking of symmetry is responsible for many physical phenomena, including the mass differences of elementary particles and phase transitions in condensed-matter systems. The breaking of mirror symmetry leads to chirality. In general, chiral effects in condensed-matter systems, such as optical activity, are associated with chiral molecular structures. But several recent observations1-3 of domain formation in thin organic films of achiral molecules have suggested that spontaneous separation into regions of differing chirality may occur in these systems. Eckhardt et al.4, meanwhile, have reported the spontaneous resolution of chiral molecules in Langmuir-Blodgett (LB) films. Here we present images of LB films of calcium arachidate obtained with the atomic force microscope5, which suggest that these achiral molecules can separate spontaneously into lattices with chiral packing of opposite handedness. We suggest that this symmetry breaking is driven by the interplay between the packing constraints imposed by the alkane tails and the molecular-area requirements set by the calcium ions 6-13.