Efficiency measurement using stochastic frontier models is well established in applied econometrics. However, no published work seems to be available on efficiency analysis using spatial data dealing with possible spatial dependence between regions. This article considers a stochastic frontier model with decomposition of inefficiency into an idiosyncratic and a spatial, spillover component. Exact posterior distributions of parameters are derived, and computational schemes based on Gibbs sampling with data augmentation are proposed to conduct simulation-based inference and efficiency measurement. The new method is illustrated using production data for Italian regions (1970–1993). Clearly, further theoretical and empirical research on the subject would be of great interest.