We introduce a nonparametric Bayesian model, called TAX, which can organize image collections into a tree-shaped taxonomy without supervision. The model is inspired by the Nested Chinese Restaurant Process (NCRP) and associates each image with a path through the taxonomy. Similar images share initial segments of their paths and thus share some aspects of their representation. Each internal node in the taxonomy represents information that is common to multiple images. We explore the properties of the taxonomy through experiments on a large (~104) image collection with a number of users trying to locate quickly a given image. We find that the main benefits are easier navigation through image collections and reduced description length. A natural question is whether a taxonomy is the optimal form of organization for natural images. Our experiments indicate that although taxonomies can organize images in a useful manner, more elaborate structures may be even better suited for this task.