The presence of occluders significantly impacts performance of systems for object recognition. However, occlusion is typically treated as an unstructured source of noise and explicit models for occluders have lagged behind those for object appearance and shape. In this paper we describe a hierarchical deformable part model for face detection and keypoint localization that explicitly models occlusions of parts. The proposed model structure makes it possible to augment positive training data with large numbers of synthetically occluded instances. This allows us to easily incorporate the statistics of occlusion patterns in a discriminatively trained model. We test the model on several benchmarks for keypoint localization including challenging sets featuring significant occlusion. We find that the addition of an explicit model of occlusion yields a system that outperforms existing approaches in keypoint localization accuracy.