Do anonymous online conversations between people with different political views exacerbate or mitigate partisan polarization? We created a mobile chat platform to study the impact of such discussions. Our study recruited Republicans and Democrats in the United States to complete a survey about their political views. We later randomized them into treatment conditions where they were offered financial incentives to use our platform to discuss a contentious policy issue with an opposing partisan. We found that people who engage in anonymous cross-party conversations about political topics exhibit substantial decreases in polarization compared with a placebo group that wrote an essay using the same conversation prompts. Moreover, these depolarizing effects were correlated with the civility of dialogue between study participants. Our findings demonstrate the potential for well-designed social media platforms to mitigate political polarization and underscore the need for a flexible platform for scientific research on social media.