The olm, a blind salamander found in cave rivers of the Balkans, is thought to live for more than 100 years but reproduces just once or twice a decade.
A female in an aquarium at the Postojna Cave has laid 50-60 eggs - and three of them are now showing signs of growth.
Nobody knows how many will hatch, or even precisely how long it will take.
"Right now it looks like three are good candidates," Saso Weldt, a biologist working at the cave, told the BBC.
He and his colleagues have taken very long-exposure photographs in the darkened cave, in order to glimpse evidence of the tiny embryos developing.
"She started laying eggs on 30 January. She is still laying one or two eggs per day, and they need something like 120 days till they hatch."
'Quite extraordinary'
That is an uncertain estimate, he explained, based on a colony of olms that was established in the 1950s in an underground lab in the French Pyrenees. There, they live in slightly warmer water, at 11C.
"In our cave, it is slightly cooler, 9C, so everything will be prolonged."
It is a unique opportunity to observe the enigmatic olm - also known as the proteus - reproducing in the same caves where it has lived for millions of years.