We present a stochastic model for metapopulations in landscapes with a finite but arbitrary number of patches. The model, similar in form to the chain-binomial epidemic models, is an absorbing Markov chain that describes changes in the number of occupied patches as a sequence of binomial probabilities. It predicts the quasi-equilibrium distribution of occupied patches, the expected extinction time (tau), and the probability of persistence (l(x)) to "age" x as a function of the number N of patches in the landscape and the number S of those patches that are suitable for the population. For a given values of N, the model shows that: (1) tau and l(x) are highly sensitive to changes in S and (2) there is a threshold value of S at which tau declines abruptly from extremely large to very small values. We also describe a statistical method for estimating model parameters from time series data in order to evaluate metapopulation viability in real landscapes. An example is presented using published data on the Glanville fritillary butterfly, Melitiaea cinxia, and its specialist parasitoid Cotesia melitaearum. We calculate the expected extinction time of M. cinxia as a function of the frequency of parasite outbreaks, and are able to predict the minimum number of years between outbreaks required to ensure long-term persistence of M. cinxia. The chain-binomial model provides a simple but powerful method for assessing the effects of human and natural disturbances on extinction times and persistence probabilities in finite landscapes. none