Supervised deep networks are among the best methods for finding correspondences in stereo image pairs. Like all supervised approaches, these networks require ground truth data during training. However, collecting large quantities of accurate dense correspondence data is very challenging. We propose that it is unnecessary to have such a high reliance on ground truth depths or even corresponding stereo pairs. Inspired by recent progress in monocular depth estimation, we generate plausible disparity maps from single images. In turn, we use those flawed disparity maps in a carefully designed pipeline to generate stereo training pairs. Training in this manner makes it possible to convert any collection of single RGB images into stereo training data. This results in a significant reduction in human effort, with no need to collect real depths or to hand-design synthetic data. We can consequently train a stereo matching network from scratch on datasets like COCO, which were previously hard to exploit for stereo. Through extensive experiments we show that our approach outperforms stereo networks trained with standard synthetic datasets, when evaluated on KITTI, ETH3D, and Middlebury. Code to reproduce our results is available at https://github.com/nianticlabs/stereo-from-mono/ .