If rising seas render small islands uninhabitable, will displaced islanders become stateless? The modern intellectual and legal tradition tells us that states must have defined, habitable territory. If so, small islands will cease to be states, and their inhabitants will accordingly become stateless. Against this, leading scholars have recently argued that the principle of presumption of continuity of state existence implies that island states continue to be states even after becoming uninhabitable. We argue to the contrary: the principle of presumption of continuity of state existence implies no such thing. If nothing is done to prevent the loss of their territory, small islands will lose their statehood, making displaced islanders stateless.