The North Atlantic northern right whale (Eubalaena glacialis) is considered the most endangered large whale species. Its population has recovered only slowly since the cessation of commercial whaling and numbers about 300 individuals. We applied mark-recapture statistics to a catalog of photographically identified individuals to obtain the first statistically rigorous estimates of survival probability for this population. Crude survival decreased from about 0.99 per year in 1980 to about 0.94 in 1994. We combined this survival trend with a reported decrease in reproductive rate into a branching process model to compute population growth rate and extinction probability. Population growth rate declined from about 1.053 in 1980 to about 0.976 in 1994. Under current conditions the population is doomed to extinction; an upper bound on the expected time to extinction is 191 years. The most effective way to improve the prospects of the population is to reduce mortality. The right whale is at risk from entanglement in fishing gear and from collisions with ships. Reducing this human-caused mortality is essential to the viability of this population.