Methods to ensure factual accuracy of text generated by large language models (LLM) in clinical medicine are lacking. VeriFact is an artificial intelligence system that combines retrieval-augmented generation and LLM-as-a-Judge to verify whether LLM-generated text is factually supported by a patient's medical history based on their electronic health record (EHR). To evaluate this system, we introduce VeriFact-BHC, a new dataset that decomposes Brief Hospital Course narratives from discharge summaries into a set of simple statements with clinician annotations for whether each statement is supported by the patient's EHR clinical notes. Whereas highest agreement between clinicians was 88.5%, VeriFact achieves up to 92.7% agreement when compared to a denoised and adjudicated average human clinican ground truth, suggesting that VeriFact exceeds the average clinician's ability to fact-check text against a patient's medical record. VeriFact may accelerate the development of LLM-based EHR applications by removing current evaluation bottlenecks.