It's likely one of them Energy Vampires, they are basically immortal in terms of age.
There was a character I planned on developing, still an NPC at this point in one of my character's plots at this point, who lived under the reign of the Rakata. Her ship did not have a realativistic shield, so when she jumped into hyperspace she ended up jumping through time as well. I don't know where that falls in regards to ageing, but relatively I imagine that makes her pretty dang old. Though as Ras pointed out, if you are looking for actually living through the years then I got nothing.
Over 20k years and counting baby.