I was informed this is the auditorium of the Bouleuterion

From the Wikipedia: A bouleuterion was a building which housed the council of citizens (boule) in Ancient Greece. There are several extant remains of Bouleuterions around Greece and former Greek territories of ancient times.

The boule, a basic institution of the ancient city-state in historical times, consisted of the citizens' representatives who assembled in order to confer and decide about public affairs. The word Bouleuterion is composed from Greek 'boule' (council) and the suffix -terion (place for doing something).