We report on a computational study of the clean and oxygen-covered Rh(110) surface, based on density-functional theory within the local-density approximation. We have used plane-wave basis sets and Vanderbilt ultra-soft pseudopotentials. For the clean surface, we present results for the equilibrium structure, surface energy and surface stress of the unreconstructed and (1 x 2) reconstructed structures. For the oxygen-covered surface we have performed a geometry optimization at 0.5, 1, and 2 monolayer oxygen coverages, and we present results for the equilibrium configurations, workfunctions and oxygen chemisorption energies. At half monolayer coverage, we find that oxygen induces a (1 x 2) reconstruction of the surface, while at one monolayer coverage the chemisorption energy is highest for the unreconstructed surface. Our results are rationalized by a simple tight-binding description of the interaction between the O 2p orbitals and the metal valence states. The resulting bonds are stronger when established with low coordinated metal atoms, and give rise to an effective adsorbate-adsorbate interaction when two oxygen atoms are bound to the same metal orbital.