Heideggerian thought is routinely understood to involve an insistence on finitude, and a rejection of the metaphysical priority of the infinite. As a general rule, this characterization isadequate, but it risks a significant oversimplification of a complex theme in Heidegger’s thinking. After an initial discussion of his dominant position on (in)finitude, the paper focuses on a number of largely neglected and some recently published texts concerning Heidegger’s retrieval of the inheritance of the Greek and Latin grammar of Being, as well as the origins of the idea of the infinite in Anaximander’s ἄπειρον. These texts reveal some important tensions in Heideggerian thought on the status of infinitude in its relation to die Sache selbst of that thought.