Online few-shot learning describes a setting where models are trained and evaluated on a stream of data while learning emerging classes. While prior work in this setting has achieved very promising performance on instance classification when learning from data-streams composed of a single indoor environment, we propose to extend this setting to consider object classification on a series of several indoor environments, which is likely to occur in applications such as robotics. Importantly, our setting, which we refer to as online few-shot continual learning, injects the well-studied issue of catastrophic forgetting into the few-shot online learning paradigm. In this work, we benchmark several existing methods and adapted baselines within our setting, and show there exists a trade-off between catastrophic forgetting and online performance. Our findings motivate the need for future work in this setting, which can achieve better online performance without catastrophic forgetting.