The rapid growth of digital health databases has attracted many researchers interested in using modern computational methods to discover and model patterns of health and illness in a research program known as computational phenotyping. Much of the work in this area has focused on traditional statistical learning paradigms, such as classification, prediction, clustering, pattern mining. In this paper, we propose a related but different paradigm called causal phenotype discovery, which aims to discover latent representations of illness that are causally predictive. We illustrate this idea with a two-stage framework that combines the latent representation learning power of deep neural networks with state-of-the-art tools from causal inference. We apply this framework to two large ICU time series data sets and show that it can learn features that are predictively useful, that capture complex physiologic patterns associated with critical illnesses, and that are potentially more clinically meaningful than manually designed features.