Understanding drivers of ecological stability is increasingly urgent amid global change. Despite ecological theory commonly assuming stable equilibria, populations in nature exhibit unstable and nonlinear dynamics, raising the question of how stability emerges from instability. The portfolio effect stabilizes ecosystems by averaging uncorrelated fluctuations, but it remains unclear whether this asynchrony is produced by stochastic perturbations of stable equilibria or deterministic nonlinear dynamics. Here we show that two globally important sockeye salmon complexes in Bristol Bay and the Fraser River are stabilized through the averaging of uncorrelated fluctuations produced by asynchronous, nonlinear population dynamics. Nonlinearity was the main source of variation as attractor reconstruction explained 61-89% of the variance in annual sockeye salmon recruitment. Furthermore, local population dynamics were primarily chaotic, but when aggregated at the regional scale where commercial fisheries operate, the dynamics stabilized and interannual variability decreased by 47%. These results indicate that portfolio effects can transform locally unstable dynamics into stable outcomes at higher levels of aggregation. Given the ubiquity of nonlinearity in nature, the averaging of uncorrelated fluctuations produced by asynchronous nonlinear dynamics may be an underappreciated mechanism driving stability in ecosystems.