An ensemble of one-year forecasts differing only in details of the atmospheric initial conditions was produced with a coupled ocean-atmosphere general circulation model (GCM) in order to investigate the predictability of the coupled system. For some ocean initial conditions, the evolution of the tropical Pacific ocean thermal structure seems to be relatively deterministic for lead times out to one year. However, there are other ocean initial conditions, mostly in the mid 1990's for which coupled model forecasts of the tropical Pacific are much more sensitive to details of the atmosphere initial conditions. In some cases, the ensemble forecasts appear to split, with some ensemble members predicting El Niño-like conditions, and others predicting La Niña. Very large ensembles were run for several of these cases. Very slight perturbations added to the atmospheric initial conditions led to large spread in predicted SST anomalies in some years. These are model results, however, they do suggest the possibility that seasonal predictions of the coupled tropical system may be highly non-deterministic in some years.