The forces between adsorbates on metals are often repulsive due to dipole-dipole interactions. Electronegative adsorbates on semiconductors, however, sometimes form clusters, exhibiting attractive interactions even though the same dipole-dipole model should apply. Here we report observations with scanning tunneling microscopy of the clustering of chlorine chemisorbed on the gallium arsenide(001)-c(8 x 2) surface. For this system, the adsorbate has been found to have an anomalously high mobility; the clustering is therefore clearly energetically favored, rather than kinetically frozen. The clustering can be understood on a purely electrostatic basis. Because the Cl-Ga bonds are not normal to the surface, clusters more closely resemble an ionic crystal than an array of dipoles. Charging of the second-neighbor Ga of the Cl adsorbate enhances this effect.