score:3
As far as I know, the answer is no. Let's look at the list of famous Ancient Greek Theaters:
Theater of Dionysus: Athens-(the oldest Greek Theater, as well as the oldest surviving Theater in the world).
Theater at Delphi
Theater at Dodona: Northwest Greece
Theater at Epidaurus-(The best preserved of all the Ancient Greek theaters): Northern Peloponnese
"Greek Theater" Taormina, Sicily-(Eastern Sicily)
The Great Theater at Ephesus-(Where Saint Paul preached, though this might have been a Roman Theater): Turkish Aegean coast
The Theater in Myra-(Saint Nicholas/(Santa Claus' town): Turkish Aegean coast
The Theater in Aspendos-(The Romans may have added a significant design to the theater's exterior/facade): South Turkish coast
All of these above mentioned Ancient Greek Theaters were built on a hilltop/ slope. Greece is a predominantly mountainous country, as is much of Turkey, as well as much of Sicily-(remember Ancient Greece once incorporated both Sicily and Turkey/Anatolia/Asia Minor into a "Greater Greece", more commonly known as, "Magna Graeca").
The only possible exceptions might be the Theater of Philippi in Northern Greece and The Theater of Syracuse in Eastern Sicily. From what I remember, both these towns have a distantly mountainous backdrop and panorama, though the theaters were not built on the traditional hilly slope. I could be wrong, though my memory is usually pretty accurate.
Upvote:3
A couple exceptions do in fact exist where the site is relatively flat and the theatre is not built into the slope of a hill or ravine but entirely built up from level ground. One such exception is Metapontum in Basilicata.