Most studies of competition in health care focus on prices and costs, but concerns about quality play a central role in policy debates. If demand is inelastic to quality, then competition may reduce patient welfare. This study uses a dataset of patient registrations for kidney transplantation in conjunction with a mixed logit model to gauge consumers' responsiveness to quality when choosing hospitals. Results indicate that at the hospital level, a one-standard deviation increase in the graft-failure rate is associated with a 6% decline in patient registrations. Privately-insured patients are more responsive to quality than Medicare patients, suggesting that insurers consider quality when contracting with providers.