SAS has round-trip flights from Chicago (ORD) to Europe (see list in the full blog post) for $365-$410 with a connection. Flights January to May.
Note: Carry on bag with a maximum weight of 18 lbs is allowed for free on SAS. You can avoid seat selection fees by accepting the randomly assigned seat at the gate.
Click for more details and booking links Cheap Flights: Chicago to Europe $365-$410 r/t – SAS