For the past quarter century, a remote corner of southwest New Zealand has provided a predator-free sanctuary for threatened species, including the world’s only flightless parrot and a lizard that’s found nowhere else on Earth.

Chalky Island, a rugged yet lush 2-square-mile outcrop in the Pacific nation’s Fiordland, is home to the endemic Te Kākahu skink, the iconic little spotted kiwi and the kākāpō, the only parrot that can’t fly and of which fewer than 250 are believed to remain in the wild.

So in August 2022, when conservation workers on the island identified a single male stoat, a weasel-like mammal native to Eurasia and North America that preys on a variety of animals and birds, they knew they had to act to save its…