An article (in greek) in Naftemporiki, and also reported by the Athens News Agency (in english, but subscription required), says that CO will start daily NYC-ATH flights on June 8th. I couldn't find any CO announcements on the issue, but here is my translation of the article:

New airlink to the USA

APE
Tuesday, 16 January, 2007

Continental Airlines is starting scheduled New York-Athens flights this summer. As was announced today by company officials, the scheduled flights will begin on June 8th and will be daily during the summer season.

The Athens - New York flight, lasting about 11 hours, will be CO105, departing Athens El. Venizelos airport at 12:20, while the return flight, lasting about 10 hours, will be CO104 and will be departing New York at 5:30 [pm].

The flights will be operated with 174 seat Boeing 767-200ER aircraft, out wich 25 seats will be in business class.

Ticket prices have not yet been determined.