Chaotic does not mean ultra-random as some people seem to think. Chaotic systems are fundamentally deterministic dynamical systems that have the property of exhibiting wildly different outcomes as a function of the initial conditions. Small errors in estimation/ measurement of initial conditions can result in unusably large differences in predicted results. If the prediction time scale is much smaller than the Lyapunov time, and initial conditions are measured with precision, predicted outcomes can have very good fidelity , and this is how they're tamed analytically.
"Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years.[19] In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random."