Ernestine Cassell, Montserrat’s tourism director, offers me a homemade guava jelly—a sticky-sweet treat that should be a signature snack for her tiny Caribbean homeland. But I’m in the modest offices of the Montserrat Tourist Board to learn more about the island’s most infamous attraction, the Soufriere Hills. It is the unavoidable elephant in the room—a smoldering, spewing, 3,740-foot-tall (and swelling) volcano that looms over every aspect of life on this beleaguered 40-square-mile speck of a British overseas territory. Since rumbling to life in mid-1995, the Soufriere Hills has buried the island’s historic capital of Plymouth and almost all of its arable land under millions of cubic yards of ash and debris, crippled Montserrat’s once robust tourist industry, driven nearly two-thirds of the population into overseas exile, and posed a dire threat to its national icon, the endemic Montserrat oriole. The 4,800 remaining islanders, such as Cassell and marketing manager...