Predicting population extinctions is a key element of quantitative conservation biology and population ecology. Although stochastic population theories have long been used to obtain theoretical distributions of population extinction times, model-based predictions have rarely been tested. Here I report results from a quantitative analysis of extinction time in 281 experimental populations of water fleas (Daphnia magna) in variable environments. To my knowledge, this is the first quantitative estimate of the shape of the distribution of population extinction times based on extinction data for any species. The finding that the distribution of population extinction times was extraordinarily peaked is consistent with theoretical predictions for density-independent populations, but inconsistent with predictions for density-dependent populations. The tail of the extinction time distribution was not exponential. These results imply that our current theories of extinction are inadequate. Future work should focus on how demographic stochasticity scales with population size and effects of nonrandom variable environments on population growth and decline.