According to Multilingual Search, quoting the Greek telecoms authority EETT, Greece is to introduce domain names expressed in the Greek alphabet in early July. The aim is apparently to boost Internet usage among Greeks who don’t always master the Latin alphabet. But it turns out to be only a half measure:

Unfortunately for the Greeks, as with other non-Latin alphabets, the step is something of a compromise as the Greek characters have to be slotted in between the protocol (http://www) and the country top level domain name (.gr).

Hard to confirm or find this news explicitly from the EETT site.