MELTING of three-dimensional solids usually starts at the free surface, which typically melts at a lower temperature than the bulk material(1). In two dimensions the starting point of many studies is the Kosterlitz-Thouless theory(2,3), in which melting is initiated through dislocation unbinding. Langmuir monolayers-single layers of amphiphilic molecules formed at the air-water interface-should provide an ideal model for studying melting in two dimensions. Here we show that for monolayer crystals of fatty acids coexisting with their liquid phase, the interior melts before the edges. The melting of crystals under mechanical stress is initiated along the line at which the internal stress vanishes. We suggest that this apparently counterintuitive result arises from defect migration to the region of zero stress, where they accumulate and nucleate melting. These results support the idea that defects play a crucial role in melting of two-dimensional systems.