In this article, I consider the influence of the ideas of Ludwig Wittgenstein, and above all the ideas of his Tractatus Logico-Philosophicus on the philosophy of logical positivism. Agreeing that the question of such an influence is not a self-evident one, I clarify at first the concept of logical positivism and then turn to the evidence of the leading logical positivists about the influence of Wittgenstein upon them. An analysis of recollections of Moritz Schlick, Rudolf Carnap, Otto Neurath, Friedrich Waismann, and Alfred Ayer suggests that at least these thinkers themselves considered such an influence as very significant.