This is true as long as at least 3 of the bodies have comparable masses, or the timescale is long enough. The periodic behavior of the Solar System is because

This is true as long as at least 3 of the bodies have comparable masses, or the timescale is long enough. The periodic behavior of the Solar System is because 99.86% of its mass is in the Sun. So every other interaction is a small rounding error. And therefore the Solar System is chaotic but with a long Lyapunov time - estimated at about 5 million years.