This has been making the rounds: a remote, Muslim community has been found speaking (and notably not writing) a dialect of Greek apparently quite close to the ancient language.
From the Independent (Jason and the Argot):
An isolated community near the Black Sea coast in a remote part of north-eastern Turkey has been found to speak a Greek dialect that is remarkably close to the extinct language of ancient Greece.
As few as 5,000 people speak the dialect but linguists believe that it is the closest, living language to ancient Greek and could provide an unprecedented insight into the language of Socrates and Plato and how it evolved.
From Katimerini (Rare Greek Dialect Alive in Turkey):
A Greek professor of linguistics at Cambridge University has been credited with identifying an endangered Greek dialect which is spoken in a remote mountainous region in northeastern Turkey and is believed to be a “linguistic gold mine” because of its close similarities to ancient Greek.
Romeyka was discovered in a remote village in the region of Trabzon (Trebizond).
Romeyka is not to be confused with Romaic, a name by which Modern Greek has been known in the past. They say that the grammar of the language itself suggests a pre-Byzantine origin, showing affinities with Koine, which is very surprising (if true).
This may be one to watch.