Global climate change is of particular concern for small and isolated populations of reptiles with temperature-dependent sex determination because low genetic variation can limit adaptive response in pivotal temperatures, leading to skewed sex ratios. We explore the demographic consequences of skewed sex ratios on the viability of a tuatara population characterized by low genetic diversity. We studied the rare species of tuatara (Sphenodon guntheri) on the 4 ha North Brother Island in New Zealand over two nesting seasons and captured 477 individuals, with a 60% male bias in the adult population. Females first breed at 15 years and have extremely low rates of gravidity, producing clutches of three to eight eggs every 9 years. Simulations of the population using population viability analysis showed that the current population is expected to persist for at least 2000 years at hatchling sex ratios of up to 75% male, but populations with 85% male hatchlings are expected to become extinct within approximately 300 years (some eight generations). Incorporation of inbreeding depression increased the probability of extinction under male biased sex ratios, with no simulated populations surviving at hatchling sex ratios >75% male. Because recent models have predicted that climate change could lead to the production of all male S. guntheri hatchlings by 2085, we examined whether periodic intervention to produce mixed or female biased sex ratios would allow the population to survive if only males were produced in natural nests. We show that intervention every 2–3 years could buffer the effects of climate change on population sex ratios, but translocation to cooler environs might be more cost-effective. Climate change threatens tuatara populations because neither modified nesting behaviour nor adaptive response of the pivotal temperature can modify hatchling sex ratios fast enough in species with long generation intervals.