Thermodynamically stable clusters containing up to 10 or more silver iodide pairs have been observed in aqueous electrolyte solutions using ultracentrifugation and cryoelectron microscopy. These clusters are in equilibrium with an excess phase of solid AgI. We measured the size distribution of the clusters by their size-dependent shift of the exciton peak at visible wavelengths and show that their statistical weight is determined by their interfacial free energy. We argue that comparable equilibrium cluster distributions, but with varying widths, must be present in all insoluble salts in contact with electrolytes that contain adsorbing potential determining ions.