We present Worldsheet, a method for novel view synthesis using just a single RGB image as input. The main insight is that simply shrink-wrapping a planar mesh sheet onto the input image, consistent with the learned intermediate depth, captures underlying geometry sufficient to generate photorealistic unseen views with large viewpoint changes. To operationalize this, we propose a novel differentiable texture sampler that allows our wrapped mesh sheet to be textured and rendered differentiably into an image from a target viewpoint. Our approach is category-agnostic, end-to-end trainable without using any 3D supervision, and requires a single image at test time. We also explore a simple extension by stacking multiple layers of Worldsheets to better handle occlusions. Worldsheet consistently outperforms prior state-of-the-art methods on single-image view synthesis across several datasets. Furthermore, this simple idea captures novel views surprisingly well on a wide range of high-resolution in-the-wild images, converting them into navigable 3D pop-ups. Video results and code are available at https://worldsheet.github.io.