We develop a simple framework to measure the role of hospital allocation in racial disparities in health care and use it to study Black and white Medicare patients who are treated for heart attacks – a condition where virtually everyone receives care, hospital care is highly effective, and hospital quality has been validated. We report four facts. (1) Black patients receive care at lower-performing hospitals than white patients, even when they live in the same hospital market or ZIP code within a hospital market. (2) Over the past two decades, the gap in performance between hospitals treating Black and white patients shrank by over two-thirds. (3) This progress is due to more rapid performance improvement at hospitals that tended to treat Black patients, rather than faster reallocation of Black patients to better hospitals. (4) Hospital performance improvement is correlated with adoption of a high-return low-cost input, beta-blockers. Closing remaining disparities in allocation and harnessing the forces of performance improvement, including technology diffusion, may be novel levers to further reduce disparities.