Habitat destruction and predation by invasive alien species has led to the disappearance of several island populations of Darwin's finches but to date none of the 13 recognized species have gone extinct. However, driven by rapid economic growth in the Galápagos, the effects of introduced species have accelerated and severely threatened these iconic birds. The critically endangered mangrove finch (Camarhynchus heliobates) is now confined to three small mangroves on Isabela Island. During 2006-2009, we assessed its population status and monitored nesting success, both before and after rat poisoning. Population size was estimated at around only 100 birds for the two main breeding sites, with possibly 5-10 birds surviving at a third mangrove. Before rat control, 54 per cent of nests during incubation phase were predated with only 18 per cent of nests producing fledglings. Post-rat control, nest predation during the incubation phase fell to 30 per cent with 37 per cent of nests producing fledglings. During the nestling phase, infestation by larvae of the introduced parasitic fly (Philornis downsi) caused 14 per cent additional mortality. Using population viability analysis, we simulated the probability of population persistence under various scenarios of control and showed that with effective management of these invasive species, mangrove finch populations should start to recover.