Alvin Fisher was back at Montefiore Health System on March 23, hospitalized again for problems related to his failing liver. He expected to be discharged the next day, but early that morning a doctor delivered the news: After 14 months, the Bronx hospital had found the 21-year-old a new liver. A man in his early 30s had died in a fall, and a team from Montefiore was heading upstate to examine the organ.

Fisher contained his emotions. "I didn't get my hopes up too much, because they could say at the last minute it was too damaged for me to have," he said.

There was reason for Fisher to be circumspect. Until then he had been behind about 30 New Yorkers waiting for a liver, giving him just a 50-50 chance of surviving long enough to get a transplant. But five weeks earlier, doctors at Montefiore had made an offer that dramatically expanded his options: He could get a liver faster if he agreed to accept one with a potentially fatal disease. He said yes.

On March 24 Fisher became the first patient in New York City to be willingly infected with hepatitis C in order to obtain a liver that might otherwise have gone to waste. For Fisher that meant taking a leap of faith that the Montefiore doctors could cure him of hep C, a blood-borne virus that could itself cause cancer and liver failure.

Fisher is among the lucky. An average of 20 people die each day in the U.S. waiting for a donated organ. With more than 14,000 people in need of a liver, demand far outstrips supply. The statistics are even worse in New York. In part because livers have a short shelf life—just eight to 12 hours from recovery to transplant—they are first allocated to a person in the donor's state or region. And because the share of New York residents who are registered organ donors is last in the nation, available organs are even harder to come by. "If Alvin had lived in another state, like Virginia or South Carolina, he would've been transplanted much sooner," said Dr. Milan Kinkhabwala, chief of transplantation at Montefiore.

Those odds have motivated doctors to push the envelope of what's an acceptable donor organ. Around the country, physicians have begun transplanting HIV-positive organs into HIV-positive patients, thanks to the reversal in 2013 of a 1998 law that banned their use. And it has become standard for transplant centers to give hep C–positive organs to patients who already have a hep C infection. Now doctors, led by those at Montefiore and a handful of other medical centers around the country, have crossed a medical threshold—and an ethical one: giving infected kidneys and livers to people who had no trace of hep C to help them get an organ sooner.

The shift is being made possible by powerful drugs approved in the past few years that can cure hepatitis C with a success rate exceeding 95%. "We probably feel the way doctors felt when penicillin was invented," said Dr. Samuel Sigal, Fisher's hepatologist, or liver specialist, at Montefiore. "Hepatitis C therapy should be considered one of the miracles of medicine. If we had not given this liver to [Fisher], he probably would've died."

One reason that more hep C–positive organs are becoming available for patients like Fisher is that many of the people who once had the disease and might have accepted an infected organ have dropped off that list because so many of them are now cured. Another factor in the supply of infected organs is the surge in the numbers of otherwise healthy younger people dying from drug abuse, particularly of opioids. Some of those individuals contracted hep C from sharing dirty needles.