We examine variation in US hospital quality across ownership, chain membership, and market concentration. We propose a new measure of quality derived from penalties imposed on hospitals under the flagship Hospital Readmissions Reduction Program, and use regression models to risk-adjust for hospital characteristics and county demographics. While the overall association between for-profit ownership and quality is negative, there is evidence of substantial heterogeneity. The quality of for-profit relative to non-profit hospitals declines with increasing market concentration. Moreover, the quality gap is primarily driven by for-profit chains. While the competition result mirrors earlier findings in the literature, the chain result appears to be new: it suggests that any potential quality gains afforded by chains are mostly realized by not-for-profit hospitals.