Numerical simulation of orbits like that of the giant comet Chiron show a distinct asymmetry between past and future. Simulations extending ±100,000 years from the present suggest that on this time-scale, Chiron is about twice as likely to have been a short-period comet at some time in the past as to become one in the future. The mean half-life for such evolution is ∼0.2 Myr, much less than the ∼l-Myr lifetime for ejection from the Solar System, implying that Chiron may have been a short-period comet in the past, and will probably become one in the future.