Levity aside... given the way medicine is progressing, the first person to become immortal has probably already been born. (probably some billionaire will be first to try it out.)

We already have anti-agathic drugs in preliminary trials, although they're more aimed at reducing the harmful effects of aging, rather than making people live longer. But you know, if you're healthier in old age, you tend to live longer anyway.

Either way, yet another instance of sci-fi becoming science fact.