I want to discuss a version of one of Zeno’s paradoxes. It is a particularly ingenious version given by José Benardete, which seems to have gone largely unnoticed... Note that Benardete’s paradox is not susceptible to resolutions of the kind standardly directed to Zenonian paradoxes of this kind. These point out that one can, in fact, do an infinite number of things in a finite time, provided only that the time interval between the actions decreases in a suitable way. Such an observation would seem to be completely irrelevant here. I don’t think that Benardete has wrung out the full force of the paradox, though. In the rest of this article I want to do just that.