The surprising discovery of a ring system around the Centaur 10199 Chariklo in 2013 led to a reanalysis of archival stellar occultation data for the Centaur 2060 Chiron by Ortiz et al. One possible interpretation of that data is that a system of rings exists around Chiron. In this work, we study the dynamical history of the proposed Chiron ring system by integrating nearly 36,000 clones of the Centaur backward in time for 100 Myr under the influence of the Sun and the four giant planets. The severity of all close encounters between the clones and planets while the clones are in the Centaur region is recorded, along with the mean time between close encounters. We find that severe and extreme close encounters are very rare, making it possible that the Chiron ring system has remained intact since its injection into the Centaur region, which we find likely occurred within the past 8.5 Myr. Our simulations yield a backward dynamical half-life for Chiron of 0.7 Myr. The dynamical classes of a sample of clones are found. It is found that, on average, the Centaur lifetimes of resonance hopping clones are twice those of random-walk clones because of resonance sticking in mean motion resonances. In addition, we present MEGNO and chaotic lifetime maps of the region bound by 13 au ≤ a ≤ 14 au and e ≤ 0.5. We confirm that the current mean orbital parameters of Chiron are located in a highly chaotic region of a - e phase space.