Are minorities treated differently by the legal system? Systematic racial differences in case characteristics, many unobservable, make this a difficult question to answer directly. In this paper, we estimate whether judges differ from each other in how they sentence minorities, avoiding potential bias from unobservable case characteristics by exploiting the random assignment of cases to judges. We measure the between-judge variation in the difference in incarceration rates and sentence lengths between African-American and White defendants. We perform a Monte Carlo simulation in order to explicitly construct the appropriate counterfactual, where race does not influence judicial sentencing. In our data set, which includes felony cases from Cook County, Illinois, we find statistically significant between-judge variation in incarceration rates, although not in sentence lengths.