We describe algorithms that use cloud shadows as a form of stochastically structured light to support 3D scene geometry estimation. Taking video captured from a static outdoor camera as input, we use the relationship of the time series of intensity values between pairs of pixels as the primary input to our algorithms. We describe two cues that relate the 3D distance between a pair of points to the pair of intensity time series. The first cue results from the fact that two pixels that are nearby in the world are more likely to be under a cloud at the same time than two distant points. We describe methods for using this cue to estimate focal length and scene structure. The second cue is based on the motion of cloud shadows across the scene; this cue results in a set of linear constraints on scene structure. These constraints have an inherent ambiguity, which we show how to overcome by combining the cloud motion cue with the spatial cue. We evaluate our method on several time lapses of real outdoor scenes.