A quantum-mechanical method is used to obtain information about the nature of bonds in chemisorption on supported metals. The calculations are based on an unidimensional model composed of a finite chain of metal atoms and a semi-infinite chain of support. The linear combination of atomic orbitals and the tight-binding approximation are used to construct the wave function of one electron in the field of the chain of metal atoms, support and chemisorbed atom. The support affects the chemisorption process, modifying the nonlocalized volume states (states with periodic wave function) and the localized states (states with non-periodic wave function); also generating new types of states in which the wave function is periodic in one layer and nonperiodic in the other (composite states). For instance, a single component finite chain of metal atoms (without support) has a single band for the volume states; with an AB-type support, the complete system can have two bands, one band or no band. The localized states can be localized at the adatom-metal surface, and/or at the metal-support interface. Also, depending upon the number of metal atoms in the chain and the nature of the support, the bond due to a localized state can change from anionic to cationic. For a composite state having wave function coefficients larger in the layer which has a periodic wave function, the electron will belong to that whole layer.