Do White and Black Americans differ in their response to fair versus unfair treatment, and do these reactions depend on whether treatment is intentional? We study an ultimatum game in which we non-deceptively vary three dimensions: racial identities of participants, offer inequality, and whether the offer was made intentionally or assigned by lottery. Unequal offers are more likely to be rejected in all conditions, but participants differed in how intentionality behind an offer affected their response. White respondents did not differentiate between intentional and randomly assigned offer inequality. In contrast, among Black respondents, intentionality increased acceptance of fair offers.