Many philosophers have argued that immortality is less good than it sounds. In this talk, I examine an argument in Jorge Luis Borges’s story “The Immortal” to the effect that immortal lives would be objectionably incoherent. Borges offers a probabilistic argument that “over an infinitely long span of time, all things happen to all [people].” I argue that Borges’s argument, suitably qualified, shows that typical mortal lives indeed exhibit a kind of incoherence. This incoherence, however, is different from the one at stake in the discussion about narrative theories of well-being, which hold that good lives have some of the virtues of good stories. Nonetheless, the incoherence of typical immortal lives makes being immortal less desirable in two respects: First, immortal lives cannot stand for something in the way mortal lives can because any commitment they might display gets superimposed by other, contradictory commitments. Second, immortal lives lack narrative intelligibility. Immortals cannot gain the kind of understanding of their own life stories that mortals can have. I illustrate both problems by way of Borges’s story and others of his writings. Finally, I briefly explore whether these shortcomings compromise the prudential value of an immortal life or some other value.