We examine variation in hospital quality across ownership, market concentration and membership of a hospital system. We use a measure of quality derived from the penalties imposed on hospitals under the flagship Hospital Readmissions Reduction Program. We employ a novel estimation approach that extracts latent hospital quality from panel data on penalties and addresses the problem of never- or always-penalized hospitals in short panels. Our quality measure correlates strongly across penalized conditions and with other non-incentivized quality metrics. We document a robust and sizable for-profit quality gap, which is largely crowded out by competition, particularly amongst high-quality and system-organized hospitals.