As reported by Loyalty Traveler, American Airlines is currently offering dirt cheap fares between Chicago and Los Angeles. Fares can be found for only $40.10 one-way for a flight of 1744 miles. That comes to just 2.3 cents per mile (its even a pretty good fare for Elite Qualifying Points at 4.6 cents per EQP). Hurry, these fare will not last long!
Dates for this fare are extremely limited. For Chicago to Los Angeles, I only see the fare on Tuesdays and Wednesdays in November.
For Los Angeles to Chicago, the fare is also available on a couple of Saturdays in November and a Tuesday in December: