Structures formed by the electrodeposition of atomic layers of chalcogenides Se and Te, on Au(100) and Au(111), are described and compared. Each element, on each surface, forms a low coverage structure, consisting of atoms packed simply in high coordinate sites at distances just above their van der Waals diameter. As coverages are increased above this level, structures composed of chalcogenide atom chains or rings are formed. It is proposed that these chains or rings have significant molecular character, involving orbital overlap of adjacent chalcogenide atoms. Mechanisms are described to account for the formation of these chains and rings. Discussion is also presented concerning the appearance of triangular phase boundaries for both chalcogenides on Au(111). In the case of Se, isolated triangles, about 4-6 nm on a side are distributed across the surface, whereas a network of triangular phase boundaries is observed in the deposition of Te. The triangular phase boundaries in Se appear to result from the nucleation of domains in different threefold sites on Au(111). For Te, however, it is proposed that the triangular domains and phase boundaries are the result of Te atoms being too large to form an extended (root 3X root 3)R30 degrees structure.