Several large earthquakes in the Hellenic subduction zone have been documented in historical records from around the eastern Mediterranean, but the relative seismic quiescence of the region over the period of instrumental observation means that the exact locations of these earthquakes and their tectonic significance are not known. We present AMS radiocarbon dates from uplifted late Holocene palaeoshorelines from the island of Rhodes, showing that uplift is most consistent with a single large (MW ≥ 7:7) reverse-faulting earthquake between about 2000 BC and 200 BC. Analysis of the uplift treating the earthquake as a dislocation in an elastic half space shows a predominantly a reverse-faulting event with a slip vector oblique to the direction of convergence between Rhodes and Nubia. We suggest that the fault responsible for the uplift dips at an angle of 30-60° above the more gently-dipping oblique subduction interface. The highly oblique convergence across the eastern Hellenic plate boundary zone appears to be partitioned into reverse slip on faults that strike parallel to the boundary and strike-parallel or oblique slip on the subduction interface. Hydrodynamical simulation of tsunami propagation from a range of tectonically plausible sources suggests that earthquakes on the fault uplifting Rhodes represent a significant tsunami hazard for Rhodes and SW Turkey, and also possibly for Cyprus and the Nile Delta.