The monastery's strange name comes, by way of generations of mispronunciation, from Hozeva or Koziva, a place in what is now Wadi Qelt near Jericho, where an Orthodox monastery of Saint George once stood. Local tradition tells that during the Byzantine Iconoclasm, when sacred images were being destroyed across the empire, an icon of the Virgin escaped by sea and washed ashore in the bay of Agia Anna, just below the cliff. The faithful built the first monastery here in the 9th century to house it. Whether the icon truly drifted across the eastern Mediterranean or not, the story has anchored this place for more than a thousand years.

The monastery steps out of legend and into documented history in 1088. In that year the Byzantine emperor Alexios I Komnenos, who reigned from 1081 to 1118, issued a chrysobull, a decree sealed in gold, granting Hozoviotissa stavropegic status, placing it directly under the patriarch rather than the local bishop. A silver liturgical fan kept inside still records that it was renovated by the great Alexios Komnenos. That imperial seal made a remote island chapel one of the most important monastic foundations in the Aegean, a status it has never lost.

Reaching the monastery means climbing 271 steps up the cliff, and the building rewards the effort with engineering that borders on the audacious. Its eight levels are linked by staircases built up or carved straight into the stone. Inside are Byzantine and pointed arches shaped from porolithos quarried on Milos, and a warren of cells, kitchens, storerooms, presses, cisterns and wells, everything a self-sufficient community needed clinging to a vertical world. The original entrance opened ten meters above the ground and was reached only by a hanging ladder that could be pulled up, a defense against pirates who plagued these waters for centuries.

The cliff that protects the monastery also threatens it. On New Year's Day in 1975, in foul weather, a landslide broke loose from the rock above and crashed down. Two boulders punched through several floors, the largest driving all the way down through three levels to the ground floor, while the refectory roof was destroyed and cracks spread through the outer walls. Urgent repairs shored up the foundations and rebuilt what was lost. Today Panagia Hozoviotissa is the patron of Amorgos, honored each November 20 and 21, and the same white monastery that drew Luc Besson's cameras in The Big Blue still glows on its cliff, improbable and unbroken.