We propose a Bayesian hierarchical model for producing probabilistic forecasts of male period life expectancy at birth for all the countries of the world from the present to 2100. Such forecasts would be an input to the production of probabilistic population projections for all countries, which is currently being considered by the United Nations. To evaluate the method, we did an out-of-sample cross-validation experiment, fitting the model to the data from 1950–1995, and using the estimated model to forecast for the subsequent ten years. The ten-year predictions had a mean absolute error of about 1 year, about 40% less than the current UN methodology. The probabilistic forecasts were calibrated, in the sense that (for example) the 80% prediction intervals contained the truth about 80% of the time. We illustrate our method with results from Madagascar (a typical country with steadily improving life expectancy), Latvia (a country that has had a mortality crisis), and Japan (a leading country). We also show aggregated results for South Asia, a region with eight countries. Free publicly available software packages called and are available to implement the method.