Knowledge distillation (KD) is an effective framework that aims to transfer meaningful information from a large teacher to a smaller student. Generally, KD often involves how to define and transfer knowledge. Previous KD methods often focus on mining various forms of knowledge, for example, feature maps and refined information. However, the knowledge is derived from the primary supervised task, and thus, is highly task-specific. Motivated by the recent success of self-supervised representation learning, we propose an auxiliary self-supervision augmented task to guide networks to learn more meaningful features. Therefore, we can derive soft self-supervision augmented distributions as richer dark knowledge from this task for KD. Unlike previous knowledge, this distribution encodes joint knowledge from supervised and self-supervised feature learning. Beyond knowledge exploration, we propose to append several auxiliary branches at various hidden layers, to fully take advantage of hierarchical feature maps. Each auxiliary branch is guided to learn self-supervision augmented tasks and distill this distribution from teacher to student. Overall, we call our KD method a hierarchical self-supervision augmented KD (HSSAKD). Experiments on standard image classification show that both offline and online HSSAKD achieves state-of-the-art performance in the field of KD. Further transfer experiments on object detection further verify that HSSAKD can guide the network to learn better features. The code is available at https://github.com/winycg/HSAKD.