The dispute over Chiron's status was when observations showed Chiron to have developed a cometary coma at perihelion! Chiron is officially both a comet and an asteroid, more proof of the very fuzzy dividing line.
Chiron is now classified as a centaur, the first of a class of objects orbiting between the outer planets. Centaurs are not in stable orbits and will eventually be removed by the giant planets. Chiron is probably a refugee from the Kuiper belt.