Aside from these fares, there are several deals from the East Coast to Europe that run in the low to mid $500 range such as Miami to Munich or Miami to Berlin. Even Chicago sees mid-$500 range fares with Chicago to Nuremberg or Chicago to Stuttgart.
Other fares from the East Coast run in the $600-750 range, while the Mid-West and West Coast fares range between $800 and $1200.
The sale is in place until October 6.
Departing flights must take place between October 11 and 29th and return travel can take place between October 12 and April 29, 2017. Tickets need to be purchased at least 21 days prior to departure and a weekend surcharge will apply if traveling between Thursday and Sunday. A Saturday night stay is required as well.
I found some flights out of Chicago and Toronto to Athens with LH, LX and OS for around $600 ish as well.