Climate change is expected to alter the distribution and abundance of many species. Predictions of climate-induced population extinctions are supported by geographic range shifts that correspond to climatic warming, but few extinctions have been linked mechanistically to climate change. Here we show that extinctions of two populations of a checkerspot butterfly were hastened by increasing variability in precipitation, a phenomenon predicted by global climate models. We model checkerspot populations to show that changes in precipitation amplified population fluctuations, leading to rapid extinctions. As populations of checkerspots and other species become further isolated by habitat loss, climate change is likely to cause more extinctions, threatening both species diversity and critical ecosystem services.