Delta attacks Star Alliance at Chicago ORD with low fares to Athens, Greece in the $541 to $572 range, available from next week to May 15, even some dates during December holidays. This deal is available every day of the week and almost every date.
United/Star Alliance has these same fares available through several airlines including Air Canada, Lufthansa, and Swiss.
You can reduce the prices even more checking Momondo.com meta-search for lower ticket prices through online travel agencies (OTAs). I found ORD-ATH $508 on my date search with United and Swiss flights and $495 for next May with Air Canada flights (see below).
Delta Airlines Chicago ORD – New York JFK – Athens, Greece ATH – Amsterdam AMS – Chicago ORD
$571.76 round trip Sun Sep 4 – Thu Sep 15
You can also book an overnight layover in Amsterdam on some dates.
United Airlines / Air Canada OTA ticket through Momondo.com search.
Chicago ORD – Montreal YUL – Athens ATH – Montreal YUL – Chicago ORD
$494.86 round trip TravelMerry.com ticket Sat May 6 – Mon May 15
Loyalty Traveler curated Airfare Deals and Google Flights and Kayak Explore tutorials.
Loyalty Traveler – Hotel Promotions Guide
Hotel loyalty program points and miles promotions for Best Western Rewards, Club Carlson, Choice Privileges, Hilton HHonors, Hyatt Gold Passport, IHG Rewards Club, Marriott Rewards, Ritz Carlton Rewards, Starwood Preferred Guest and Wyndham Rewards.
