The introduction of Anolis cristatellus from the multiple species anole community of Puerto Rico in the Greater Antilles to the island of Dominica in the Lesser Antilles, with its solitary endemic anole, provides an example of a very recent, timed, single introduction. We investigate the geographic origin and adaptive potential of the Dominican population using a range of methods including mtDNA phylogeography, nuclear microsatellite variation and multiple paternity studies, as well as heritability estimates, common garden experiments and comparative geographic studies of quantitative scalation traits. Phylogeographic analysis of NADH2 and microsatellite studies suggests that the Dominican population arose from a set of individuals from the central west area of Puerto Rico within their endemic range. The multiple-individual inoculation, together with sperm storage and evidence of multiple paternity indicate genetic variability and suggest the potential for adaptation by natural selection. Estimates of heritability, common garden experiments and broad sense QST/FST ratios, linked to replicated comparisons along elevational transects go some way to suggesting that the invasive populations may be adapting by natural selection, in parallel with the endemic anole, in the brief period since their introduction.