We present the first model to optimize patient selection for lung transplantation from the perspective of the transplant center. In 2007, the Centers for Medicare and Medicaid Services (CMS) introduced regulations designed to improve medical outcomes at transplant centers by financially penalizing transplant centers with high one-year post-transplant mortality rates. Since then, much work has focused on optimal allocation of organs within organ donation networks, but none has focused on optimizing the center-level patient mix in order to comply with CMS regulations. We introduce a chance-constrained non-linear mixed-integer programming model to maximize the number of patients who receive a transplant, while constraining the risk of penalization by the CMS. In addition, our model can be used to model dynamic pay-for-performance systems, which have seen growing popularity in the medical context. The present work may contribute to significant medical cost reduction and improve post-surgery survival rates for transplant recipients, thereby serving to keep more transplant centers open.