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We propose CoRE, a 360° video streaming approach that reduces bandwidth requirements compared to transferring the entire 360° video. CoRE uses non-linear sampling in both the spatial and temporal domains to achieve robustness to view direction prediction error and to transient wireless network bandwidth fluctuation. Each CoRE frame samples the environment in all directions, with full resolution over the predicted field of view and gradually decreasing resolution at the periphery, so that missing pixels are avoided, irrespective of the view prediction error magnitude. A CoRE video chunk has a main part at full frame rate, and an extension part at a gradually decreasing frame rate, which avoids stalls while waiting for a delayed transfer. We evaluate a prototype implementation of CoRE through trace-based experiments and a user study, and find that, compared to tiling with low-resolution padding, CoRE reduces data transfer amounts, stalls, and H.264 decoding overhead, increases frame rates, and eliminates missing pixels.