Thank you for this, waybread.
It relates the myth as
Kheiron was a renowned teacher who mentored many of the greatest heroes of myth ... [and]
was accidentally wounded by Herakles when the hero was battling other members of the tribe. The wound, poisoned with Hydra-venom, was incurable, and suffering unbearable pain Kheiron voluntarily relinquished his immortality. Zeus then placed him amongst the stars as the constellation Sagittarius or Centaurus.
He didn't just relinquish his mortal side, he took the place of Prometheus, thereby releasing the god who gave the gift of fire to humankind, and was being tortured by Zeus.