For all the talk lately about privilege, few have commented on the moral obligations associated with having privilege. Those who have commented have not gone much beyond the idea that the privileged should be conscious of their privilege and should listen to those who do not have it. Here we want to go further and build an account of the moral obligations of those with a particular kind of privilege: race privilege. In this paper, we articulate an understanding of race privilege, show how a person can know when she has it and argue that a race-privileged person has obligations to offset her privilege. We make concrete suggestions for how she can, at least approximately, do this. We use particular racial-group disparities in the United States as our running example throughout the paper, although our conclusions generalize.