An interesting option to visit USA even during peak season in summer 2015 is available with Alitalia and their partners. Return flights from Germany (Berlin) to Chicago would cost you just €361.An interesting alternative would be an open jaw ticket that allows you to visit New York and Chicago during your US trip. In such case you may book your flight already for €439 which is still an amazing fare considering this is within peak season..
In some cases there is longer layover in Rome and could be a great solution to visit this beautiful city on your way to America. In case of booking please look for flights departing from Germany till 10th of July or from 18th of August 2015 till end of January 2016. As there is long layover in Rome on your return flight this also gives you an option to end your trip there and not to continue to Germany.
Travel dates are the easiest to check here using +- 3 days searching tool.
Booking sample of cheap flights to Chicago from Germany in summer 2015 for €361. In this case you would be departing from Berlin to Chicago on 7th of July. Your return flight from USA back to Germany would be then on 23rd of July 2015.