The initial situation actually starts off stage, before the play begins: Prometheus is really ticked off that Zeus is tyrannizing over the Titans and wants to kill off the humans, so he steals fire from Mt. Olympus. Thanks, dude! When the play opens, we see the result of this situation: Prometheus is chained up to a rock. Guess this is a game with high stakes.
Only in an Ancient Greek tragedy would trying to make peace actually become conflict. Oceanus comes to make peace between Prometheus and Zeus, but it's a no go: Prometheus isn't in this for himself. He has to keep waging the war, and peacemakers like Oceanus just get in the way.
Things get a bit complicated when a new character charges on stage: the mortal princess Io, who is looking a little bovine these days. At first, it's not even clear what she's doing here—did she just wander in from another play, or what? And why is the whole middle section of Prometheus Bound now being taken up with Prometheus delivering prophecies about Io's future?
Prometheus finally announces that one of Io's descendants is destined to free him. Since this little revelation clarifies Io's connection to the play, it ties the story together. Way to go, Prometheus!
Just when things start looking up—even if that's not going to be until hundreds of years in the future—Hermes shows up with a message from Zeus: Prometheus better talk, or else.
Prometheus takes "else." Our man in Scythia sends the ambassador of the gods packing, calling him a menial servant for good measure.
So, since this play isn't called "Prometheus Triumphant" or anything hopeful like that, it's not too surprising that he ends up falling down into the center of the earth. But wait! There's hope. Thanks to all the prophecy, we know that this isn't the end of our intrepid rebel.
Prometheus, Part II, coming to an Athenian stage near you. (And guess what? One of Prometheus's gifts to humanity was just that—hope.)