The Chauvet cave is unique because its preservation is unprecedented ? despite containing the oldest paintings ever discovered. Comma?

Your sentence is unclear, but—at the very least—you have a misplaced modifier.

Your prepositional phrase—despite containing the oldest paintings ever discovered—is meant to modify the Chauvet Cave—that thing that contains the oldest paintings ever discovered.

You need to move the prepositional phrase next to the cave:

Despite containing the oldest paintings ever discovered, the Chauvet Cave is unique because its preservation is unprecedented.
or
The Chauvet Cave, despite containing the oldest paintings ever discovered, is unique because its preservation is unprecedented.

My hunch is that you are trying to say something more like this:

Despite being the oldest cave paintings ever discovered, the Chauvet Cave paintings are preserved like no others.