As an order, Parrots (Psittaciformes) are both the longest lived birds and among the most endangered. Palm Cockatoos (Probosciger aterrimus) have an extremely slow life history, including one of the lowest rates of breeding success reported for parrots. Here we use population viability analysis (PVA) to examine whether populations of Palm Cockatoos are viable in the long term with such low rates of reproduction. We built PVA models for two field sites with robust data on reproductive success and availability of nest-hollows: Iron Range on Cape York Peninsula (Queensland, Australia) and Crater Mountain (Eastern Highlands Province, Papua New Guinea). Our Iron Range models incorporate a fluctuating resource base of nest-hollows resulting from natural losses from fire, wind and tree decay and natural replenishment through tree breakages in tropical cyclones. The number of females allowed to breed each year in the simulations was limited by the availability of hollows. Our Iron Range models suggest that the population is only viable if juvenile and adult mortality rates are very low, and that at least some birds in the population live to 100 years old. Based on known maximum lifespans in the Cacatuidae, we conclude that Palm Cockatoos at Iron Range are unlikely to live for long enough on average to support their low rates of reproduction, and highlight the possibility that the population may be in decline. At Crater Mountain, where nestlings are harvested for food by local people, the models suggest that the reported current rate of 40% of nestlings taken is not sustainable.