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Racial disparities in policing have been a subject of intense interest throughout the history of American politics. Recent events have focused attention on the use of lethal force against Black Americans. Evaluating whether observed patterns can be attributed to racial bias has proven difficult, though, because of the lack of systematic data and inability to properly account for confounding factors that influence the use of lethal force. We develop a formal model of civilian-police interactions and shootings that identifies a test for racial bias that relies on fatality rates, conditional upon shootings. We present original data on all officer-involved shootings from three American cities. Our analysis finds evidence of racial bias against Black civilians in the decision to use lethal force. We quantify how many Black Americans have been shot by police officers who would not have been shot were they White Americans.