In his lecture course on Parmenides, Heidegger calls Anaximander, Parmenides and Heraclitus primordial thinkers (anfangliche Denker). He makes a distinction between early thinkers and primordial thinkers. Not every early Greek thinker is a primordial thinker for him. The primordial thinker is one who thinks the beginning (Anfang), and for Heidegger the beginning is being (Sein). Anaximander, Parmenides and Heraclitus are primordial thinkers, Heidegger says, not just because they initiate Western thought (there were also other thinkers at that time who did so), but because they think the beginning. The reason why Heidegger pays so much attention to Anaximander, Parmenides and Heraclitus in his works is thus clear. They stir his interest because they are the only Presocratic thinkers whom he considers primordial, who think the beginning which is being. But what does it mean to think the beginning? We know the reasons why Heidegger wishes to undertake his study of the Presocratics. He attempts to bring our thinking back to being and to the possibilities for being that are offered by the Presocratic thought. This is consistent with his view of history and philosophy. Still, what does he mean by saying that the Presocratic thinkers think the beginning? Why is the beginning being? What can we learn from the Heideggerian interpretation of the Presocratics? In this paper I attempt to answer these questions by examining Heidegger's readings of the Anaximander fragment. His commentary on this oldest recorded philosophical text of the West is best known from his essay "The Anaximander Fragment" (Der Spruch des Anaximander), written in 1946 and first published in Holzwege in 1950. However, Heidegger also discussed the Anaximander fragment in his lectures, first in 1926 and then in 1941. I take into consideration all these sources. I show that if the 1926 lecture still largely depends on traditional Presocratic scholarship, his 1941 lecture and 1946 essay are a radical departure from it. Further, I argue that for its right comprehension the later Heidegger's interpretation of Anaximander has to be placed in the wider context of his original philosophy of history-the history of being.