People can learn a new visual class from just one example, yet machine learning algorithms typically require hundreds or thousands of examples to tackle the same problems. Here we present a Hierarchical Bayesian model based on compositionality and causality that can learn a wide range of natural (although simple) visual concepts, generalizing in human-like ways from just one image. We evaluated performance on a challenging one-shot classification task, where our model achieved a human-level error rate while substantially outperforming two deep learning models. We also used a "visual Turing test" to show that our model produces human-like performance on other conceptual tasks, including generating new examples and parsing.