Recent breakthroughs in self-supervised learning show that such algorithms learn visual representations that can be transferred better to unseen tasks than cross-entropy based methods which rely on task-specific supervision. In this paper, we found that the similar holds in the continual learning context: contrastively learned representations are more robust against the catastrophic forgetting than ones trained with the cross-entropy objective. Based on this novel observation, we propose a rehearsal-based continual learning algorithm that focuses on continually learning and maintaining transferable representations. More specifically, the proposed scheme (1) learns representations using the contrastive learning objective, and (2) preserves learned representations using a self-supervised distillation step. We conduct extensive experimental validations under popular benchmark image classification datasets, where our method sets the new state-of-the-art performance. Source code is available at https://github.com/chaht01/Co2L.