Right now, February/2020 is the most affordable month to take a flight to Chicago. The most expensive time of year is July/2020.
Qantas Airways and American Airlines fly non-stop between Australia and Chicago.
The cheapest airline to fly from Australia to Chicago is American Airlines.
The best airline to fly from Australia to Chicago is Qatar Airways. For direct flights then Qantas Airways is best. The best budget airline is WestJet.