UA actaully does not fly from Chicago to India. That was a pipe dream from one of the executives from a few years ago.
To see how an airline might fly a route, you might want to look at:
http://gc.kls2.com
The "Great Circle Mapper" is a cool site that shows you how an airline might fly from ORD-NRT. You'll notice that it's much less "polar" than ORD-HKG.