Modern generative AI systems have shown the capacity to produce remarkably fluent language, prompting debates both about their semantic understanding and, less prominently, about whether they can perform speech acts. This paper addresses the latter question, focusing on assertion. We argue that to be capable of assertion, an entity must meet two requirements: it must produce outputs with descriptive functions, and it must be capable of being sanctioned by agents with which it interacts. The second requirement arises from the nature of assertion as a norm-governed social practice. Pre-trained large language models that have not been subject to fine-tuning fail to meet the first requirement. Language models that have been fine-tuned for “groundedness” or “correctness” may meet the first requirement, but fail the second. We also consider the significance of the point that AI systems can be used to generate proxy assertions on behalf of human agents.