Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of these randomized methods for use with data sets that are too large to be stored in random-access memory (RAM). (The traditional terminology is that our procedure works efficiently "out-of-core.") We illustrate the performance of the algorithm via several numerical examples. For example, we report on the PCA of a data set stored on disk that is so large that less than a hundredth of it can fit in our computer's RAM.