Large language models are now able to generate content- and genre-appropriate prose with grammatical sentences. However, these targets do not fully encapsulate human-like language use. For example, set aside is the fact that human language use involves sociolinguistic variation that is regularly constrained by internal and external factors. This article tests whether one widely used LLM application, ChatGPT, is capable of generating such variation. I construct an English corpus of “sociolinguistic interviews” using the application and analyze the generation of seven morphosyntactic features. I show that the application largely fails to generate any variation at all when one variant is prescriptively incorrect, but that it is able to generate variable deletion of the complementizer that that is internally constrained, with variants occurring at human-like rates. ChatGPT fails, however, to properly generate externally constrained complementizer that deletion. I argue that these outcomes reflect bias both in the training data and Reinforcement Learning from Human Feedback. I suggest that testing whether an LLM can properly generate sociolinguistic variation is a useful metric for evaluating if it generates human-like language.