The latest generation of neural networks has made major performance advances in object categorization from raw images. In particular, deep convolutional neural networks currently outperform alternative approaches on standard benchmarks by wide margins and achieve human-like accuracy on some tasks. These engineering successes present an opportunity to explore long-standing questions about the nature of human concepts by putting psychological theories to test at an unprecedented scale. This paper evaluates deep convolutional networks trained for classification on their ability to predict category typicality -- a variable of paramount importance in the psychology of concepts -- from the raw pixels of naturalistic images of objects. We find that these models have substantial predictive power, unlike simpler features computed from the same massive dataset, showing how typicality might emerge as a byproduct of a complex model trained to maximize classification performance.