Islands are found to spontaneously form on the GaAs(001)-(2X4) reconstructed surface. The geometry and size of these islands are examined as a function of substrate temperature and island coverage. Both the islands' coverage and size increase with increasing temperature. The islands are elongated rectangles and the aspect ratio is independent of temperature. A relationship between the islands' aspect ratio and the step formation energies is presented. These results are also related to recent theoretical work on equilibrium island geometry.