Trust is essential for a secure and flourishing social life, but many economic and philosophical approaches argue that rational people should never extend it, in particular to strangers they will never encounter again. Emerging data on the trust game, a laboratory economic exchange, suggests that people trust strangers excessively (i.e., far more than their tolerance for risk and cynical views of their peers should allow). What produces this puzzling "excess" of trust? We argue that people trust due to a norm mandating that they show respect for the other person's character, presuming the other person has sufficient integrity and goodwill even if they do not believe it privately. Six studies provided converging evidence that decisions to trust follow the logic of norms. Trusting others is what people think they should do, and the emotions associated with fulfilling a social duty or responsibility (e.g., guilt, anxiety) account for at least a significant proportion of the excessive trust observed. Regarding the specific norm in play, trust rates collapse when respect for the other person's character is eliminated as an issue.