In the winter of 2015, Dr. Tom Chiller received a call from public-health officials in Britain.

They were panicking. A new fungus was causing devastating infections at a large London hospital. “They weren’t able to get rid of it,” says Chiller, who was then chief of the fungal-diseases branch at the U.S. Centers for Disease Control and Prevention (CDC). “They didn’t know what to do.”

The British officials said the fungus—a kind of yeast called Candida auris—appeared to be spreading from patient to patient. The officials said they were going to shut down parts of the hospital to curb its transmission. “That was just mind-boggling,” Chiller says.

At first he was more confused than alarmed. Candida is a kind of yeast that causes some of the most common fungal conditions, including thrush and vaginal yeast infections. Some species can cause severe illnesses, including bloodstream infections.…