Agni Parthene (O Virgin Pure)

It is not ancient (as you might have suspected given the harrmonies) but 19th C and western-influenced. The poem is by Bishop Nectarios of Aegina, who was recognised as a saint in 1961. The isolated church that shows up around the 4:30 mark reminds me of one we visted at Stina da Vale in Transylvania, well up in the mountains.