LAX to Chicago or reverse route is priced at $54 each way with United Airlines for travel dates March to May 2019. Most availability is in March.
Another feature of this sale are low one way fares from some California regional airports, which feed into LAX flights. Monterey to Chicago and Chicago to Monterey is $88 each way on United.
United Airlines Los Angeles LAX – Chicago ORD – LAX
United Airlines Chicago ORD – Los Angeles LAX – Monterey MRY – LAX – ORD