Do large language models (LLMs) know the law? These models are increasingly being used to augment legal practice, education, and research, yet their revolutionary potential is threatened by the presence of hallucinations -- textual output that is not consistent with legal facts. We present the first systematic evidence of these hallucinations, documenting LLMs' varying performance across jurisdictions, courts, time periods, and cases. Our work makes four key contributions. First, we develop a typology of legal hallucinations, providing a conceptual framework for future research in this area. Second, we find that legal hallucinations are alarmingly prevalent, occurring between 58% of the time with ChatGPT 4 and 88% with Llama 2, when these models are asked specific, verifiable questions about random federal court cases. Third, we illustrate that LLMs often fail to correct a user's incorrect legal assumptions in a contra-factual question setup. Fourth, we provide evidence that LLMs cannot always predict, or do not always know, when they are producing legal hallucinations. Taken together, our findings caution against the rapid and unsupervised integration of popular LLMs into legal tasks. Even experienced lawyers must remain wary of legal hallucinations, and the risks are highest for those who stand to benefit from LLMs the most -- pro se litigants or those without access to traditional legal resources.