Abstract Kidneys are the most prevalent organ transplants, but demand dwarfs supply. Kidney exchanges enable willing but incompatible donor-patient pairs to swap donors. These swaps can include cycles longer than two pairs as well, and chains triggered by altruistic donors. Current kidney exchanges address clearing (deciding who gets kidneys from whom) as an offlfline problem: they optimize the current batch. In reality, clearing is an online problem where patient-donor pairs and altruistic donors appear and expire over time. In this paper, we study trajectory-based online stochastic optimization algorithms (which use a recent scalable optimal of- flfline solver as a subroutine) for this. We identify tradeoffs in these algorithms between different parameters. We also uncover the need to set the batch size that the algorithms consider an atomic unit. We develop an experimental methodology for setting these parameters, and conduct experiments on real and generated data. We adapt the REGRETS algorithm of Bent and van Hentenryck for the setting. We then develop a better algorithm. We also show that the AMSAA algorithm of Mercier and van Hentenryck does not scale to the nationwide level. Our best online algorithm saves signifificantly more lives than the current practice of solving each batch separately