Chapel encourages McCoy to reveal that he is dying of xenopolycythemia
Xenopolycythemia was a rare blood disease associated with unusual hemoglobin and white corpuscle counts. It caused excessive proliferation of red blood cells in the Human body. The disease was always fatal within a year if not treated early. The cure, possessed by the Fabrini in the 23rd century, was extremely uncomfortable, and the drug had to be administered in small doses at specific intervals during the treatment period. When given in time, recovery was 100%.
In 2152, when Captain Archer was kidnapped and put on trial by the Klingon Empire, Doctor Phlox told them that Archer had xenopolycythemia, a ruse that allowed him to meet with the captain. To convince the guard to leave, Phlox described the disease as highly contagious, and said that they should have put Archer in quarantine. (ENT: "Judgment")
In the 2150s, a sample of this disease's pathogen was stored at Cold Station 12. (ENT: "Cold Station 12")
In 2268, Dr. McCoy was diagnosed with xenopolycythemia. He believed himself to only have a year to live, which he told Captain James T. Kirk, asking him to keep this news to himself. Because of this, he was susceptible to the chance for happiness which marriage to Natira, the Fabrini high priestess, afforded him. After Spock discovered a cure among the technological lore of the Fabrini, McCoy separated from his wife and returned to the USS Enterprise. Nurse Chapel administered a hypospray with the new medication, and reported that his white corpuscle count was back to normal. Spock, after consulting his tricorder, added that "your hemoglobin count is back to normal, doctor, which indicates that the flow of oxygen to each cell of your body is back up to its abundantly energetic level." (TOS: "For the World is Hollow and I Have Touched the Sky").
The Star Trek Concordance described xenopolycythemia as characterized by excessive proliferation of red blood cells, similar to the Earthly condition polycythemia which causes sluggish blood flow to the extremities, and clots which can lead to heart attack or stroke. Star Trek: Lost Scenes showed a scene in which Spock describes the disease as causing granulation of hemoglobin. On Earth, polycythemia is not contagious; it is usually caused by a genetic mutation, or is secondary to other conditions that increase blood production hormones or reduce oxygen levels in the bloodstream.
The name of the disease is derived from the classical Greek "xeno" (foreign) + "poly" (many) + "cythemia" (involving blood cells).
In the Mirror Universe story The Sorrows of Empire, the Enterprise-Fabrini encounter was either hostile or never occurred, and McCoy's counterpart soon died from the disease.