On October 5, 1988, Chileans decided by plebiscite to oust General Pinochet from power and have free presidential elections in 1989. This article describes the projections that the authors made for the results of the plebiscite from early returns. From a statistical point of view, what made these projections different from those made in other countries was the complete lack of historic data. Furthermore, the Pinochet government carried out a campaign to discredit the projection effort. Uncertainty about both the data and the unpredictable political climate on the night of the plebiscite influenced the choice of the statistical methodology. The predictions, based on a 10% sample of the first one-third of the votes counted, were within one-half a percentage point of the true outcome. The described methodology could prove useful in projections of other elections that will take place under similar conditions (e.g., in Eastern Europe).