Biological invasions are a major global threat to biodiversity and often affect ecosystem services negatively. They are particularly problematic on oceanic islands where there are many narrow-ranged endemic species, and the biota may be very susceptible to invasion. Quantifying and mapping invasion processes are important steps for management and control but are challenging with the limited resources typically available and particularly difficult to implement on oceanic islands with very steep terrain. Remote sensing may provide an excellent solution in circumstances where the invading species can be reliably detected from imagery. We here develop a method to map the distribution of the alien chestnut (Castanea sativa Mill.) on the island of La Palma (Canary Islands, Spain), using freely available satellite images. On La Palma, the chestnut invasion threatens the iconic laurel forest, which has survived since the Tertiary period in the favourable climatic conditions of mountainous islands in the trade wind zone. We detect chestnut presence by taking advantage of the distinctive phenology of this alien tree, which retains its deciduousness while the native vegetation is evergreen. Using both Landsat 8 and Sentinel-2 (parallel analyses), we obtained images in two seasons (chestnuts leafless and in-leaf, respectively) and performed image regression to detect pixels changing from leafless to in-leaf chestnuts. We then applied supervised classification using Random Forest to map the present-day occurrence of the chestnut. Finally, we performed species distribution modelling to map the habitat suitability for chestnut on La Palma, to estimate which areas are prone to further invasion. Our results indicate that chestnuts occupy 1.2% of the total area of natural ecosystems on La Palma, with a further 12–17% representing suitable habitat that is not yet occupied. This enables targeted control measures with potential to successfully manage the invasion, given the relatively long generation time of the chestnut. Our method also enables research on the spread of the species since the earliest Landsat images.