Automatic Chemical Design is a framework for generating novel molecules with optimized properties. The original scheme, featuring Bayesian optimization over the latent space of a variational autoencoder, suffers from the pathology that it tends to produce invalid molecular structures. First, we demonstrate empirically that this pathology arises when the Bayesian optimization scheme queries latent space points far away from the data on which the variational autoencoder has been trained. Secondly, by reformulating the search procedure as a constrained Bayesian optimization problem, we show that the effects of this pathology can be mitigated, yielding marked improvements in the validity of the generated molecules. We posit that constrained Bayesian optimization is a good approach for solving this kind of training set mismatch in many generative tasks involving Bayesian optimization over the latent space of a variational autoencoder.