We compute probabilities for future great earthquakes in the Aleutian arc. Probability distributions are fitted to recurrence periods of great Aleutian evens (Mw≥7.8) since 1788. Given a probability distribution and data of the last grat earthquake in each arc segment, time-dependent conditional probabilities are determined for future periods of interest. We obtain for the next two decades high probabilities (99 to 30%) for great earthquakes in the Shumagin, Yakataga, Unalaska and Kommandorski seismic gaps. These probabilities are higher than for any other assessed region of the U.S. believed to be capable of great earthquakes. Low probabilities (17 to 9%) are found for segments that ruptured most recently in 1965, 1964 and 1957. Recurrence periods for great earthquakes measure on average about 80 years but vary substantially. Whether recurrence periods for great Aleutian earthquakes follow a normal, log-normal or any other probability distribution is not resolved because in most arc segments the known seismic record embraces at best one or two recurrences. The resulting uncertainty affects the magnitude of estimated probabilities, especially in seismic gaps that have not ruptured for a long time. In some instances a normal distribution yields a three times higher probability than the corresponding log-normal distribution.