United Airlines has a competitive fare to Spirit and Frontier for Los Angeles to Chicago, although far fewer dates each month at $119 round trip than Spirit Airlines.
Low fares are available for travel from September to February. Sep-Oct have most availability for travel dates.
Los Angeles LAX – Chicago ORD – Los Angeles LAX
Aside: I am disappointed to see American and United have both changed their ticket display during the past year. New design makes it difficult to take a compact image of itinerary and fare, thus I used the easier to read Google Flights display above.