We propose continual entropy minimization (CENT) to adapt computer vision models to continual distribution shifts at ImageNet scale. CENT leverages a replay buffer with images from the source distribution along with rolling parameter buffers to stabilize the training dynamics of conventional test-time adaptation methods. Our work is the first to demonstrate stable, continual adaptation on ImageNet scale, and obtains state-of-the-art results in both static and continual variants of the ImageNet-C benchmark.