The brown treesnake (Boiga irregularis) population on the Pacific island of Guam has reached iconic status as one of the most destructive invasive species of modern times, yet no published works have used genetic data to identify a source population. We used DNA sequence data from multiple genetic markers and coalescent-based phylogenetic methods to place the Guam population within the broader phylogeographic context of B. irregularis across its native range and tested whether patterns of genetic variation on the island are consistent with one or multiple introductions from different source populations. We also modeled a series of demographic scenarios that differed in the effective size and duration of a population bottleneck immediately following the invasion on Guam, and measured the fit of these simulations to the observed data using approximate Bayesian computation. Our results exclude the possibility of serial introductions from different source populations, and instead verify a single origin from the Admiralty Archipelago off the north coast of Papua New Guinea. This finding is consistent with the hypothesis thatB. irregularis was accidentally transported to Guam during military relocation efforts at the end of World War II. Demographic model comparisons suggest that multiple snakes were transported to Guam from the source locality, but that fewer than 10 individuals could be responsible for establishing the population. Our results also provide evidence that low genetic diversity stemming from the founder event has not been a hindrance to the ecological success of B. irregularis on Guam, and at the same time offers a unique ‘genetic opening’ to manage snake density using classical biological approaches.