Although racial/ethnic disparities in health have been well-characterized in biomedical, public health, and social science research, the determinants of these disparities are still not well-understood. Chronic psychosocial stress related specifically to the American experience of institutional and interpersonal racial discrimination may be an important determinant of these disparities, as a growing literature in separate scientific disciplines documents the adverse health effects of stress and the greater levels of stress experienced by non-White compared to White Americans. However, the empirical literature on the importance of stress for health and health disparities specifically due to racial discrimination, using population-representative data, is still small and mixed. In this paper, we explore the association between a novel measure of racially-salient chronic stress - "racism-related vigilance" - and sleep difficulty. We found that, compared to the White adults in our sample, Black (but not Hispanic) adults reported greater levels of vigilance. This vigilance was positively associated with sleep difficulty to similar degrees for all racial/ethnic groups in our sample (White, Black, Hispanic). Black adults reported greater levels of sleep difficulty compared to White adults. This disparity was slightly attenuated after adjustment for education and income. However, this disparity was completely attenuated after adjustment for racism-related vigilance. We found similar patterns of results for Hispanic compared to White adults, however, the disparities in sleep difficulty were smaller and not statistically significant. Because of the importance of sleep quality to health, our results suggest that the anticipation of and perseveration about racial discrimination is an important determinant of racial disparities in health.