We have performed a detailed dynamical study of the recently identified Neptunian Trojan 2004 KV18, only the second object to be discovered librating around Neptune's trailing Lagrange point, L5. We find that 2004 KV18 is moving on a highly unstable orbit, and was most likely captured from the Centaur population at some point in the last ∼1 Myr, having originated in the scattered disc, beyond the orbit of Neptune. The instability of 2004 KV18 is so great that many of the test particles studied leave the Neptunian Trojan cloud within just ∼0.1–0.3 Myr, and it takes just 37 Myr for half of the 91 125 test particles created to study its dynamical behaviour to be removed from the Solar system entirely. Unlike the other Neptunian Trojans previously found to display dynamical instability on 100-Myr time-scales (2001 QR322 and 2008 LC18), 2004 KV18 displays such extreme instability that it must be a temporarily captured Trojan, rather than a primordial member of the Neptunian Trojan population. As such, it offers a fascinating insight into the processes through which small bodies are transferred around the outer Solar system, and represents an exciting addition to the menagerie of the Solar system's small bodies.