Kick'em Jenny is a submarine volcano situated 9 kilometres north of Grenada in the Lesser Antilles. A preliminary study suggests that the volcano is a prime candidate for tsunamigenic eruptions on a potentially hazardous scale, possibly affecting the whole of the Eastern Caribbean region. The uniqueness of individual volcanic eruptions means that attempts to generalise tsunamigenic mechanisms are extremely tentative. However, the theory of underwater explosion generated water waves is applicable to submarine volcanoes to model explosive eruptions. Using this theory, initial maximum ocean surface displacements are calculated for Kick'em Jenny hydroeruptions, corresponding to various event magnitudes (up to a lsquoworst-casersquo scenario eruption on the scale of Krakatau, 1883). Wave propagation theories are then applied to the resulting tsunami wave dispersion, before beach shoaling equations are used to estimate the maximum tsunami run-up at adjacent coastal areas. Maps of the region have been prepared showing the paths of the wave-fronts (ray-tracing), travel times and maximum wave run-up amplitudes along coastlines. Finally, an attempt is made to assess how great a hazard the volcano represents, by considering the probability of each magnitude event occurring.