Interpersonal conflict is an uncomfortable but unavoidable fact of life. Navigating conflict successfully is a skill -- one that can be learned through deliberate practice -- but few have access to effective training or feedback. To expand this access, we introduce Rehearsal, a system that allows users to rehearse conflicts with a believable simulated interlocutor, explore counterfactual "what if?" scenarios to identify alternative conversational paths, and learn through feedback on how and when to apply specific conflict strategies. Users can utilize Rehearsal to practice handling a variety of predefined conflict scenarios, from office disputes to relationship issues, or they can choose to create their own setting. To enable Rehearsal, we develop IRP prompting, a method of conditioning output of a large language model on the influential Interest-Rights-Power (IRP) theory from conflict resolution. Rehearsal uses IRP to generate utterances grounded in conflict resolution theory, guiding users towards counterfactual conflict resolution strategies that help de-escalate difficult conversations. In a between-subjects evaluation, 40 participants engaged in an actual conflict with a confederate after training. Compared to a control group with lecture material covering the same IRP theory, participants with simulated training from Rehearsal significantly improved their performance in the unaided conflict: they reduced their use of escalating competitive strategies by an average of 67%, while doubling their use of cooperative strategies. Overall, Rehearsal highlights the potential effectiveness of language models as tools for learning and practicing interpersonal skills.