The text of this inaugural lecture proposes that the newly established A. G. Leventis Professorship of Greek Culture is a new kind of chair: a chair not only for research but also for outreach, for the advancement of the public understanding of ancient Greek culture. After explaining its origins, and pondering the possible meanings of the Professorship's title, it seeks to explore four 'myths' about the ancient Greeks and their culture (or cultures), myths deliberately chosen to illustrate the huge range of the Hellenic tradition that is still actively at work in our own culture. These are: i. that there was an entity called 'Ancient Greece'; ii. that the ancient Greeks were technologically backward; iii. that the ancient Greeks really were (or looked) anything like they are depicted in such movies as 300; and iv. that the Greeks invented democracy in anything like the form in which we understand it today.