This paper uses measles incidence in developed countries as the basis of a case study in nonlinear forecasting and chaos. It uses a combination of epidemiological modelling and nonlinear forecasting to explore a range of issues relating to the predictability of measles before and after the advent of mass vaccination. A comparison of the pre-vaccination self-predictability of measles in England and Wales indicates relatively high predictability of these predominantly biennial epidemic series, compared to New York City, which shows mixtures of one-, twoand three-year epidemics. This analysis also indicates the importance of choosing correct embeddings to avoid bias in prediction. Forecasting for English cities indicates significant spatial heterogeneity in predictability before vaccination and an overall drop in predictability during the vaccination era. The interpretation of predictions of observed measles series by epidemiological models is explored and areas for refinement of current models discussed.