The adsorption of a single monolayer of GaAs on the (110) surface of Si has been studied by first principles total-energy calculations. We have used the density functional theory, within the local density approximation. It is found that As and Ga atoms are adsorbed on Si(110) following a relaxation pattern similar to clean group-III--group-V (110) surfaces. Arsenic atoms move outwards while Ga atoms are pushed down. The surface is ordered, and the periodicity remains (1\ifmmode\times\else\texttimes\fi{}1). We have also investigated the possible diffusion of Ga and/or As atoms into the Si substrate. Mixed Si-Ga, Si-As or an embedded Ga-As layer are not favorable energetically. The most stable configuration corresponds to the GaAs monolayer on top of the Si(110) substrate. Interchanging the GaAs overlayer by GaSb (with a lattice constant 13% larger than Si) results in a disordered surface.