Any Star Trek fanatics out there?

I saw an episode of what I'm pretty sure was Star Trek a long time ago and I've always wanted to see the episode again since. I need to know if it was indeed ST and if so maybe what the episode was called or anything that can help me find it. Basically in the episode they come across this race that ages backwards. They are born old and become babies before dying. I think they might be sent into a cave or something at the end of their lives to die. Anyone know anything about this?