Tame behaviour, i.e. low wariness, in terrestrial island species is often attributed to low predation pressure. However, we know little about its physiological control and its flexibility in the face of predator introductions. Marine iguanas (Amblyrhynchus cristatus) on the Galapagos Islands are a good model to study the physiological correlates of low wariness. They have lived virtually without predation for 5-15 Myr until some populations were first confronted with feral cats and dogs some 150 years ago. We tested whether and to what extent marine iguanas can adjust their behaviour and endocrine stress response to novel predation threats. Here, we show that a corticosterone stress response to experimental chasing is absent in naive animals, but is quickly restored with experience. Initially, low wariness also increases with experience, but remains an order of magnitude too low to allow successful escape from introduced predators. Our data suggest that the ability of marine iguanas to cope with predator introductions is limited by narrow reaction norms for behavioural wariness rather than by constraints in the underlying physiological stress system. In general, we predict that island endemics show flexible physiological stress responses but are restricted by narrow behavioural plasticity.