From observations on individually marked limpets (Acmaea digitalis) in their natural environment along the coast of Central Oregon, it has been possible to design a test of the hypothesis that they have a home range. The test depends on comparison of the limpets'' observed spatial distribution after a period of 7 months with that expected on the hypothesis that they believe like particles diffusing at random but with rates corresponding with those observed over shorter periods of time. The random walk hypothesis does not fit the data well, and the deviation is in the direction of infradispersion. A suitable statistical test of significance of the deviation does not seem to exist.