I don't fly out of Chicago but Boston.
I normally fly with Delta and for years there was no non-stop flight to Athens. I had a layover somewhere, usually JFK or worse London or Paris. It not only made the day extra long but the flight(s) seemed forever.
Thankfully Delta finally started non-stop from Boston to Athens last year and while somewhat higher it made all the difference in the world not having to stop somewhere, deplane, go to the next gate, either walk or a take a shuttle, and then wait anywhere from 2-3 hours for the flight to Athens.
It's worth the extra money to take the non-stop flight.
I find it less expensive to book as many months out as you can rather than waiting the closer you get to your departure.
I spent $980 for a non-stop flight to Athens by booking last January! The flight now is anywhere from $600-$700 more!