Caesium lead iodide is of interest both as a photoluminescent material whose optical properties may be tuned by creating nanoscale structures, and as an inorganic analogue of the recently developed solar cell sensitiser methylammonium lead iodide. Rietveld refinement of the high-temperature perovskite phase of this material gives unreasonable atomic displacement parameters on the I atoms, suggesting that the local symmetry of these sites is less than implied by the spatially averaged structure. We propose to collect total scattering data from this material; reverse Monte Carlo refinement will produce a model consistent with the local as well as the average structure. Our results will help to elucidate structure-property relationships in both this specific material and the broader lead halide perovskite family, as well as the development of the RMC technique itself.