The seismic potential of the Chilean and southern Peruvian margins of South America is reevaluated to delineate those areas or segments of the margin that may be expected to experience large or great interplate earthquakes within the next 20 years (1984--2004). Long-term estimates of seismic potential (or the conditional probability of recurrence within a specified period of time) are based on (1) statistical analysis of historic repeat time data using Weibull distributions and (2) deterministic estimates of recurrence times based on the time-predictable model of earthquake recurrence. Both methods emphasize the periodic nature of large and great earthquake recurrence, and are compared with estimates of probability based on the assumption of Poisson-type behavior. The estimates of seismic potential presented in this study are long-term forecasts only, as the temporal resolution (or standard deviation) of both methods is taken to range from ¿15% to ¿25% of the average or estimated repeat time. At present, the Valparaiso region of central Chile (32¿--35¿S) has a high potential or probability of recurrence in the next 20 years. Coseismic uplift data associated with previous shocks in 1822 and 1906 suggest that this area may have already started to rerupture in 1971--1973. Average repeat times also suggest this area is due for a great shock within the next 20 years. Flanking segments of the Chilean margin, Coquimbo-Illapel (30¿--32¿S) and Talca-Concepcion (35¿--38¿S), presently have poorly constrained but possibly quite high potentials for a series of large or great shocks within the next 20 years. In contrast, the rupture zone of the great 1960 earthquake (37¿--46¿S) has the lowest potential along the margin and is not expected to rerupture in a great earthquake within the next 100 years. In the north, the seismic potentials of the Molendo-Arica (17¿--18¿S) and Arica-Antofagasta (18¿--24¿S) segments (which last ruptured during great earthquakes in 1868 and 1877) are also high, but poorly constrained.