I'd recommend pluggin in a few city pairs into Orbitz, Travelocity or one of the other on-line travel sites and seeing what you come up with. On Orbitz, you can tell them you prefer non-stops, and they can search on those, in addition to the connecters. Surely United and American fly Chicago to various California destinations. SWA is probably cheaper, (but not always). Go see for yourself.
Good luck!