The interfacial structure of well-defined Pd(lll) single-crystal electrodes in 0.05 M H2SO4 has been studied by electrochemical scanning tunneling microscopy (EC-STM) at potentials within the electrical double-layer region. Experiments with (virtually) atomically sharp STM tips yielded images of such quality that the intermolecular and intramolecular structures of the highly ordered compact layer could actually be resolved on an atomic scale. Fundamental concepts in inorganic chemistry have been invoked to postulate that SO42-, H3O+, and H2O are the most likely constituents of the compact layer. A structural model of such a compact layer is presented.