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We introduce the task of local relighting, which changes a photograph of a scene by switching on and off the light sources that are visible within the image. This new task differs from the traditional image relighting problem, as it introduces the challenge of detecting light sources and inferring the pattern of light that emanates from them. We propose an approach for local relighting that trains a model without supervision of any novel image dataset by using synthetically generated image pairs from another model. Concretely, we collect paired training images from a stylespace-manipulated GAN; then we use these images to train a conditional image-to-image model. To benchmark local relighting, we introduce Lonoff, a collection of 306 precisely aligned images taken in indoor spaces with different combinations of lights switched on. We show that our method significantly outperforms baseline methods based on GAN inversion. Finally, we demonstrate extensions of our method that control different light sources separately. We invite the community to tackle this new task of local relighting.