Air India has round-trip flights from Chicago (ORD) to Hyderabad (HYD) for $674 with a connection. Flights in September. Departures on Monday, Tuesday, Wednesday, and Sunday.
Some small OTAs on Skyscanner and Google have this for as low as $601; which is cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.