The occurrence of the Indian Ocean Tsunami on 26 December, 2004 has raised concern about the difficulty in determining appropriate tsunami mitigation measures in Australia, due to the lack of information on the tsunami threat. A first step in the development of such measures is a tsunami hazard assessment, which gives an indication of which areas of coastline are most likely to experience tsunamis, and how likely such events are. Here we present the results of a probabilistic tsunami hazard assessment for Western Australia (WA). Compared to other parts of Australia, the WA coastline experiences a relatively high frequency of tsunami occurrence. This hazard is due to earthquakes along the Sunda Arc, south of Indonesia. Our work shows that large earthquakes offshore of Java and Sumba are likely to be a greater threat to WA than those offshore of Sumatra or elsewhere in Indonesia. A magnitude 9 earthquake offshore of the Indonesian islands of Java or Sumba has the potential to significantly impact a large part of the West Australian coastline. The level of hazard varies along the coast, but is highest along the coast from Carnarvon to Dampier. Tsunamis generated by other sources (e.g., large intra-plate events, volcanoes, landslides and asteroids) were not considered in this study.