Inverse rendering of outdoor scenes from unconstrained image collections is a challenging task, particularly illumination/albedo ambiguities and occlusion of the illumination environment (shadowing) caused by geometry. However, there are many cues in an image that can aid in the disentanglement of geometry, albedo and shadows. Whilst sky is frequently masked out in state-of-the-art methods, we exploit the fact that any sky pixel provides a direct observation of distant lighting in the corresponding direction and, via a neural illumination prior, a statistical cue to derive the remaining illumination environment. The incorporation of our illumination prior is enabled by a novel ‘outside-in’ method for computing differentiable sky visibility based on a neural directional distance function. This is highly efficient and can be trained in parallel with the neural scene representation, allowing gradients from appearance loss to flow from shadows to influence the estimation of illumination and geometry. Our method estimates high-quality albedo, geometry, illumination and sky visibility, achieving state-of-the-art results on the NeRF-OSR relighting benchmark. Our code and models can be found at https://github.com/JADGardner/neusky .