There is a species of jellyfish called Turritopsis nutricula has been proven to be biologically capable of immortality by repeatedly reverting to its earlier polyp stage, effectively re-starting its life-cycle and so reversing ageing. In theory it can repeat this indefinitely.
If we could find out how to copy this process....
Also, Li Qingyun is on public record as being over 250 years old and he was quite open about his "secrets" of longevity. Also, he stated that he has regularly met monks up in the mountains that were well over 500 years old. So certainly extreme lifespans are possible. But immortality?