Artificial neural networks are well-known to be susceptible to catastrophic forgetting when continually learning from sequences of tasks. Various continual (or incremental) learning approaches have been proposed to avoid catastrophic forgetting, but they are typically adversary agnostic, i.e., they do not consider the possibility of a malicious attack. In this effort, we explore the vulnerability of Elastic Weight Consolidation (EWC), a popular continual learning algorithm for avoiding catastrophic forgetting. We show that an intelligent adversary can take advantage of EWC's continual learning capabilities to cause gradual and deliberate forgetting by introducing small amounts of misinformation to the model during training. We demonstrate such an adversary's ability to assume control of the model via injection of backdoor attack samples on both permuted and split benchmark variants of the MNIST dataset. Importantly, once the model has learned the adversarial misinformation, the adversary can then control the amount of forgetting of any task. Equivalently, the malicious actor can create a false memory about any task by inserting carefully-designed backdoor samples to any fraction of the test instances of that task. Perhaps most damaging, we show this vulnerability to be very acute; the model memory can be easily compromised with the addition of backdoor samples into as little as 1% of the training data of even a single task.