The process of drug discovery involves a search over the space of all possible chemical compounds. Generative Adversarial Networks (GANs) provide a valuable tool towards exploring chemical space and optimizing known compounds for a desired functionality. Standard approaches to training GANs, however, can result in mode collapse, in which the generator primarily produces samples closely related to a small subset of the training data. In contrast, the search for novel compounds necessitates exploration beyond the original data. Here, we present an approach to training GANs that promotes incremental exploration and limits the impacts of mode collapse using concepts from Genetic Algorithms. In our approach, valid samples from the generator are used to replace samples from the training data. We consider both random and guided selection along with recombination during replacement. By tracking the number of novel compounds produced during training, we show that updates to the training data drastically outperform the traditional approach, increasing potential applications for GANs in drug discovery.