Most existing star-galaxy classifiers use the reduced summary information from catalogs, requiring careful feature extraction and selection. The latest advances in machine learning that use deep convolutional neural networks allow a machine to automatically learn the features directly from data, minimizing the need for input from human experts. We present a star-galaxy classification framework that uses deep convolutional neural networks (ConvNets) directly on the reduced, calibrated pixel values. Using data from the Sloan Digital Sky Survey (SDSS) and the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), we demonstrate that ConvNets are able to produce accurate and well-calibrated probabilistic classifications that are competitive with conventional machine learning techniques. Future advances in deep learning may bring more success with current and forthcoming photometric surveys, such as the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST), because deep neural networks require very little, manual feature engineering.