Based on this paragraph, give me a summary of what a kidney donor chain is.

Context: Exchanges and chains are a novel approach to expand the living donor pool. In February 2012, this novel approach to expand the living donor pool resulted in the largest chain in the world, involving 60 participants organized by the National Kidney Registry. In 2014 the record for the largest chain was broken again by a swap involving 70 participants. The acceptance of altruistic donors has enabled chains of transplants to form. Kidney chains are initiated when an altruistic donor donates a kidney to a patient who has a willing but incompatible donor. This incompatible donor then 'pays it forward' and passes on the generosity to another recipient who also had a willing but incompatible donor. Michael Rees from the University of Toledo developed the concept of open-ended chains. This was a variation of a concept developed at Johns Hopkins University. On 30 July 2008, an altruistic donor kidney was shipped via commercial airline from Cornell to UCLA, thus triggering a chain of transplants. The shipment of living donor kidneys, computer-matching software algorithms, and cooperation between transplant centers has enabled long-elaborate chains to be formed.


Answer: When a donor wishes to give their kidney to a specific patient but they are not a match with that patient, they can join a kidney donor chain to accelerate the process of finding an organ for the patient. In exchange for giving their kidney to another patient, the patient they had wanted to help can be paired with another donor who is a match for them but not for the patient to whom they wish to donate their kidney.