Rebuilt by the Romans to hold 15,000 spectators (one of the largest of the ancient world), the Greek Theater dates back to the fifth century b.c. when Aeschylus himself arrived from his home at Gela to supervise productions of his tragedies.
The Greek Theater was constructed in the fifth century b.c.
Although his tragedies were performed in the Greek Theater, Aeschylus didn't supervise any productions.