Invasive freshwater fish represent a major threat to biodiversity. Here, we first demonstrate the dramatic, human-mediated range expansion of the Trinidadian guppy (Poecilia reticulata), an invasive fish with a reputation for negatively impacting native freshwater communities. Next, we explore possible mechanisms that might explain successful global establishment of this species. Guppies, along with some other notable invasive fish species such as mosquitofish (Gambusia spp.), have reproductive adaptations to ephemeral habitats that may enable introductions of very small numbers of founders to succeed. The remarkable ability of single pregnant guppies to routinely establish viable populations is demonstrated using a replicated mesocosm set up. In 86% of cases, these populations persisted for two years (the duration of the experiment). Establishment success was independent of founder origin (high and low predation habitats), and there was no loss of behavioural performance amongst mesocosm juveniles. Behavioural "signatures" of the founding locality were, however, evident in mesocosm fish. Our results demonstrate that introductions consisting of a single individual can lead to thriving populations of this invasive fish and suggest that particular caution should be exercised when introducing this species, or other livebearers, to natural water bodies.