Random thinning has been shown to produce useful diagnostics for assessing the goodness-of-fit of a temporal or space-time point process model. The technique involves keeping or deleting each point individually, with each point kept with a probability inversely proportional to the conditional intensity at that point. This method does not extend immediately to the case of a purely spatial point process defined by its Papangelou intensity, however. Here, a method for thinning a spatial point process into a Poisson process is introduced. The proposed technique involves considering each possible subset of points, and keeping or deleting the subset with the appropriate probability. A demonstration on a simulated clustered spatial point process is considered, and practical implications and shortcomings are discussed.