One of the core goals of a universal health care system is to eliminate discrimination on the basis of socioeconomic status. We test for discrimination using patient waiting times for non-emergency treatment in public hospitals. Waiting time should reflect patients clinical need with priority given to more urgent cases. Using data from Australia, we find evidence of prioritisation of the richest patients, especially the least urgent, who can be delayed with lower health risks, thereby allowing more scope for discrimination. The rich also benefit from variation in supply endowments. These results challenge the universal system's core principle of equitable treatment.