We present a Deep Image Compression neural network that relies on side information, which is only available to the decoder. We base our algorithm on the assumption that the image available to the encoder and the image available to the decoder are correlated, and we let the network learn these correlations in the training phase. Then, at run time, the encoder side encodes the input image without knowing anything about the decoder side image and sends it to the decoder. The decoder then uses the encoded input image and the side information image to reconstruct the original image. This problem is known as Distributed Source Coding in Information Theory, and we discuss several use cases for this technology. We compare our algorithm to several image compression algorithms and show that adding decoder-only side information does indeed improve results. Our code is publicly available at https://github.com/ayziksha/DSIN.