We present a low-energy electron diffraction and Auger electron spectroscopy (AES) study of the growth of Al and Ga chains on Si(112) substrates. For substrate temperatures between 500 and 650-degrees-C growth proceeds first by the creation of metal atom chains along the step edges of the (112) surface. Once the step-edge sites have been occupied, a state defined here as "saturation coverage," excess deposition leads to island formation with no further increase in the metal AES signal intensity. The clean Si(112) (1 X 2) surface reconstruction is removed upon the formation of the metal chains so that the equivalence of adjacent single-layer-height steps is restored. At the saturation coverage both the Al and Ga chains exhibit a sixfold periodicity along the step edge, or [110BAR], direction. Below the saturation coverage these chains can also exhibit a fivefold periodicity along the same direction. We propose a model in which the periodicities of the chains are determined by the density of dimerized Si edge atoms, i.e, metal atom vacancies, whose presence balances the tensile stress imposed by the larger metal atoms. We investigate the relative binding energies of Al and Ga to the step-edge sites and find that Al atoms are more strongly bound. At substrate temperatures near 600-degrees-C die deposition of Al on a Ga saturated surface leads to the complete substitution of Ga by Al atoms at the step-edge sites.