Clinical trials are often hindered by the challenge of patient recruitment. In this work, we introduce TrialGPT, a first-of-its-kind large language model (LLM) framework to assist patient-to-trial matching. Given a patient note, TrialGPT predicts the patient's eligibility on a criterion-by-criterion basis and then consolidates these predictions to assess the patient's eligibility for the target trial. We evaluate the trial-level prediction performance of TrialGPT on three publicly available cohorts of 184 patients with over 18,000 trial annotations. We also engaged three physicians to label over 1,000 patient-criterion pairs to assess its criterion-level prediction accuracy. Experimental results show that TrialGPT achieves a criterion-level accuracy of 87.3% with faithful explanations, close to the expert performance (88.7%-90.0%). The aggregated TrialGPT scores are highly correlated with human eligibility judgments, and they outperform the best-competing models by 32.6% to 57.2% in ranking and excluding clinical trials. Furthermore, our user study reveals that TrialGPT can significantly reduce the screening time (by 42.6%) in a real-life clinical trial matching task. These results and analyses have demonstrated promising opportunities for clinical trial matching with LLMs such as TrialGPT.