This paper develops and analyzes a queueing model to examine the role of patient choice on the high rate of organ refusals in the kidney transplant waiting system. The model is an M/M/1 queue with homogeneous patients and exponential reneging. Patients join the waiting system and organ transplants are reflected by the service process. In addition, unlike the standard M/M/1 model, each service instance is associated with a variable reward that reflects the quality of the transplant organ, and patients have the option to refuse an organ (service) offer if they expect future offers to be better. Under an assumption of perfect and complete information, it is demonstrated that the queueing discipline is a potent instrument that can be used to maximize social welfare. In particular, first-come-first-serve (FCFS) amplifies patients’ desire to refuse offers of marginal quality, and generates excessive organ wastage. By contrast, last-come-first-serve (LCFS) contains the inefficiencies engendered by patient choice and achieves optimal organ utilization. A numerical example calibrated using data from the U.S. transplantation system demonstrates that the welfare improvements possible from a better control of patient choice are equivalent to a 25% increase in the supply of organs.