This paper studies wealth distribution dynamics in a small open economy with a continuum of consumers indexed by initial wealth. Each of them solves a discrete-choice problem whose optimal policy function exhibits ergodic chaos. We show that for any initial distribution of wealth given by a density, the wealth distribution converges to a unique invariant distribution, and aggregate wealth converges to the corresponding value. Thus ergodic chaos leads to aggregate stability rather than instability. These results are illustrated with various numerical examples.