We present a new replay-based method of continual classification learning that we term "conditional replay" which generates samples and labels together by sampling from a distribution conditioned on the class. We compare conditional replay to another replay-based continual learning paradigm (which we term "marginal replay") that generates samples independently of their class and assigns labels in a separate step. The main improvement in conditional replay is that labels for generated samples need not be inferred, which reduces the margin for error in complex continual classification learning tasks. We demonstrate the effectiveness of this approach using novel and standard benchmarks constructed from MNIST and FashionMNIST data, and compare to the regularization-based \textit{elastic weight consolidation} (EWC) method.