A two-dimensional lattice gas model is used to study oxygen-vacancy ordering in the basal plane of YBa2Cu3O7-δ. Various stable and metastable configurations are determined by Landau-Lifshitz theory and through Monte Carlo simulations. An analysis of the appropriate Landau-Ginzburg-Wilson Hamiltonian shows that the critical behavior corresponds to the universality class of the Ashkin-Teller model. A phase diagram and short and long range order parameters are calculated by means of Kikuchi's cluster variation method. At high and intermediate temperatures, comparison with experiment is excellent.