The view synthesis problem—generating novel views of a scene from known imagery—has garnered recent attention due in part to compelling applications in virtual and augmented reality. In this paper, we explore an intriguing scenario for view synthesis: extrapolating views from imagery captured by narrow-baseline stereo cameras, including dual-lens camera phones and VR cameras. We call this problem stereo magnification, and propose a new learning framework that leverages a new layered representation that we call multiplane images (MPIs), as well as a massive new data source for learning view extrapolation: online videos on YouTube. Using data mined from such videos, we train a deep network that predicts an MPI from an input stereo image pair. This inferred MPI can then be used to synthesize a range of novel views of the scene, including views that extrapolate significantly beyond the input baseline. We show that our method compares favorably with several recent view synthesis methods, and demonstrate applications in magnifying narrow-baseline stereo images.