We propose to reinterpret a standard discriminative classifier of $p(y | \x)$ as an energy based model for the joint distribution $p(\x, y)$. In this setting, the standard class probabilities can be easily computed as well as unnormalized values of $p(\x)$ and $p(\x|y)$. Within this framework, standard discriminative architectures may be used and the model can also be trained on unlabeled data. We demonstrate that energy based training of the joint distribution improves calibration, robustness, and out-of-distribution detection while also enabling our models to generate samples rivaling the quality of recent GAN approaches. We improve upon recently proposed techniques for scaling up the training of energy based models and present an approach which adds little overhead compared to standard classification training. Our approach is the first to achieve performance rivaling the state-of-the-art in both generative and discriminative learning within one hybrid model.