It is important for autonomous vehicles to have the ability to infer the goals of other vehicles (goal recognition), in order to safely interact with other vehicles and predict their future trajectories. This is a difficult problem, especially in urban environments with interactions between many vehicles. Goal recognition methods must be fast to run in real time and make accurate inferences. As autonomous driving is safety-critical, it is important to have methods which are human interpretable and for which safety can be formally verified. Existing goal recognition methods for autonomous vehicles fail to satisfy all four objectives of being fast, accurate, interpretable and verifiable. We propose Goal Recognition with Interpretable Trees (GRIT), a goal recognition system which achieves these objectives. GRIT makes use of decision trees trained on vehicle trajectory data. We evaluate GRIT on two datasets, showing that GRIT achieved fast inference speed and comparable accuracy to two deep learning baselines, a planning-based goal recognition method, and an ablation of GRIT. We show that the learned trees are human interpretable and demonstrate how properties of GRIT can be formally verified using a satisfiability modulo theories (SMT) solver.