Devastating tsunami emphasize the vulnerability of low-lying islands and coasts. Our risk assessment for the three atolls of Tokelau uses computer simulations of tsunami generated by a series of regional and distant earthquakes to inform a community advisory of a threat from tsunami flooding. Great earthquakes off northeastern Japan pose a potential threat, with maximum wave heights >  1 m, but villages remain dry. Informative simulation studies can be achieved on atolls with only basic field data.