In 1971, he was appointed chairman of the Department of Surgery at NewYork–Presbyterian Hospital and Columbia University College of Physicians and Surgeons, where he was involved in developing a multidisciplinary approach to transplant services, as well as advocating surgical repair and reconstruction as an alternative to radical excision.

He had one older sister, Carol, and from 1938 was raised on a Navajo reservation in Arizona when he attended a one-room school house which taught only to eighth grade.

[7] This, combined with Reemtsma's belief in that the lack of previous successful attempts should not deter innovation,[6][8] led him to explore the possibility of primate-to-human transplantation.

[6] Between 5 November 1963 and 10 February 1964,[6] whilst professor of surgery at Tulane University, Louisiana, Reemtsma performed a series of chimpanzee-to-human kidney transplants.

[10] Retired from space-flight or the circus, bad-tempered or no longer wanted, both kidneys from six chimpanzees were transplanted into six people who had terminal renal failure,[6][9] using the 'en bloc' technique, where the two kidneys with their accompanying blood vessels (including aorta and vena cava) were implanted and joined to the recipient's external iliac artery and external iliac vein.

[3] One female school teacher, admitted with chronic glomerulonephritis and severe uraemia in November 1963 at the age of 23, had the chimpanzee kidney transplant procedure performed on 13 January 1964.

[5] In 1963, James Hardy, who had carried out the first human lung allotransplant, visited Reemtsma and was impressed by the outcome of the chimpanzee kidney transplantations.

[5] In 1964, at the American Surgical Association meeting in Hot Springs, Virginia, where he presented Tulane's experience of early xenotransplants, including the one patient surviving nine months, he was met with mixed emotions.

He recruited Willem Kolff,[1] the surgeon who, as a young doctor in the Nazi-occupied Netherlands during the Second World War, invented the first dialysis machine using sausage casings and an automobile water pump part.

Reemtsma and surgical colleague Eric Rose further developed the New York-Presbyterian Hospital transplant services on the principles of a multidisciplinary cooperation between surgeons, nephrologists, immunologists and others.

[14] At a time when heart transplants were controversial and were only being performed by Norman Shumway at Stanford University, and Richard Lower in Virginia, Reemtsma was committed and succeeded in strengthening Columbia's cardiac residency training programme.

[1] Reemtsma frequently reiterated the story about how owing to his service in Korea, and his behavior and build, he was the model for "Hawkeye Pierce" in Richard Hooker's novel MASH.