Hmm... Tricky question.
There is no central, national body that issues general filming permits in Greece and the need to get one depends on where you want to shoot.
The Hellenic Film Commission, run by the Greek Film Centre, may be contacted to issue a letter to facilitate filming, as well as a certificate that a project is suitable for filming in Greece (i.e. not in breach of national legislation). Both these documents are then included in the application to other national or regional archeological, municipal, military or other relevant authorities in order to acquire the right permit in each case.
But it is much simpler than it sounds. In general, if you are going to film in public locations you only need permission from the relevant municipal authority (usually without cost, with the exception of the city of Athens and some highly touristic places, i.e. Santorini). If you want to film in a private space, you only need permission from the property owner. If however you want to film in or near an archeological space or monument, then you need to get permissions form the Ministry of Culture, a process that takes at least one month. Accordingly, if your locations include military sites, national parks or other areas of special interest, the relative authority will have to be contacted in advance.
And don’t you worry. We have long-term experience in getting film permits for any type of filming in a timely and efficient manner, as well as well-established local contacts to grand you and your project immediate access wherever possible.