The Siberian chipmunk is native to north-eastern Asia, but alien populations of this squirrel, introduced through the pet trade, occur in many European countries. This rodent has been listed as an invasive species of European concern, being a potential vector of ticks spreading Lyme disease. We aimed to assess its current distribution range and to identify areas of potential invasion. Two sets of species distribution models were conducted, one considering the locations of the species (n = 625 occurrences) and the other with only the occurrences of the Korean subspecies (the invasive one in Europe; n = 255 occurrences), which might be a separate species from the Siberian one. We included 19 uncorrelated predictors (two topographic, nine land cover, five bioclimatic and three anthropogenic variables), which may represent the habitat characteristics of the target species. Most of the northern hemisphere supports the establishment of the Siberian chipmunk, particularly for the invasive Korean subspecies (especially in Europe, where it is already established), mostly in urban areas. Anthropogenic food supply was found to be an important factor promoting the growth of alien populations of chipmunks, whereas the presence of the native red squirrel at the time of introduction may limit it.