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.