Work on continual learning (CL) has thus far largely focused on the problems arising from shifts in the data distribution. However, CL can be decomposed into two sub-problems: (a) shifts in the data distribution, and (b) dealing with the fact that the data is split into chunks and so only a part of the data is available to be trained on at any point in time. In this work, we look at the latter sub-problem, the chunking of data. We show that chunking is an important part of CL, accounting for around half of the performance drop from offline learning in our experiments. Furthermore, our results reveal that current CL algorithms do not address the chunking sub-problem, only performing as well as plain SGD training when there is no shift in the data distribution. Therefore, we show that chunking is both an important and currently unaddressed sub-problem and until it is addressed CL methods will be capped in performance. Additionally, we analyse why performance drops when learning occurs on identically distributed chunks of data, and find that forgetting, which is often seen to be a problem due to distribution shift, still arises and is a significant problem. We also show that performance on the chunking sub-problem can be increased and that this performance transfers to the full CL setting, where there is distribution shift. Hence, we argue that work on chunking can help advance CL in general.