Social media are frequently blamed for exacerbating ideological divides. We evaluate whether it is possible to design a social media platform that instead promotes productive, open-minded dialogue among users. We recruited 1,043 Americans who expressed willingness to test a new social media platform by installing a mobile app we developed for iOS and Android devices. Participants were randomly assigned to spend ten minutes on one of two versions of a simulated social media platform. The first was a control condition designed to resemble typical text-based social media sites, and users were told that people whose posts are liked very often receive a “popular user” badge. The second version was identical to the first, but respondents were instead told users receive an “open-minded” badge if they respectfully engage with opposing viewpoints. Participants using both versions were asked to join an ongoing discussion about either gun control or immigration. Unbeknownst to them, each participant only interacted with chatbots powered by generative AI. We find that respondents assigned to the experimental condition exhibited more intellectually humble language in their posts and comments and reported experiencing more positive emotions. We do not find significant treatment effects on participants’ self-reported intellectual humility, affective polarization, or issue attitudes. These results have important implications for future research on social media and social psychology and introduce new methods for conducting randomized controlled trials using generative artificial intelligence.