A solid-state chemical model is given for the production of O2 by electronic excitation of ice, a process that occurs on icy bodies in the outer solar system. Based on a review of the relevant available laboratory data, we propose that a trapped oxygen atom-water complex is the principal precursor for the formation of molecular oxygen in low-temperature ice at low fluences. Oxygen formation then occurs through direct excitation of this complex or by its reaction with a freshly produced, nonthermal O from an another excitation event. We describe a model for the latter process that includes competition with precursor destruction and the effect of sample structure. This allows us to put the ultraviolet photon, low-energy electron, and fast-ion experiments on a common footing for the first time. The formation of the trapped oxygen atom precursor is favored by the preferential loss of molecular hydrogen and is quenched by reactions with mobile H. The presence of impurity scavengers can limit the trapping of O, leading to the formation of oxygen-rich molecules in ice. Rate equations that include these reactions are given and integrated to obtain an analytic approximation for describing the experimental results on the production and loss of molecular oxygen from ice samples. In the proposed model, the loss rate varies, roughly, inversely with solid-state defect density at low temperatures, leading to a yield that increases with increasing temperature as observed. Cross sections obtained from fits of the model to laboratory data are evaluated in light of the proposed solid-state chemistry.