A grotto in the cliff face, the Choragic Monument of Thrasyllos was built here around 320 BC. In the Christian era it became the Chapel of Our Lady of the Cavern; old pictures and icons cover the walls. Above the chapel two slender Ionic columns are the remains of Thrasyllos' monument. It's open only on 15 August, the day of the Dormition of the Virgin.
It's above the Theatre of Dionysos, accessible by a path east from the Asclepieion. The path gives a good view down on to the theatre; you can make out the marble diamond pattern on the stage.