As well as the big three transcontinentals, American, TWA and United, a fourth nonstop operator was Continental, who had been given authority for the route when their 707 jets first came along. THe CAB typically licensed up to three operators on the main trunk routes, I can't think of another where they allowed a fourth.

Continental only had a handful of 707s when these flights started, which also included Chicago to Denver and Denver to LAX, and they operated them in a novel, highly intensive manner, where periodic maintenance checks, which traditionally required the aircraft being put in the hangar for a day or so every week, were broken down into a series of smaller tasks which were worked on in turn each night. It allowed them to schedule all their fleet every day. By 1968 though their fleet had rolled over, the original turbojet 707s had gone, and their jet flights were mainly run with 720Bs. They had also built up a substantial fleet of 707-320Cs as well, but these were principally used on military charters to Vietnam, Continental, along with Braniff and Pan Am, having been early operators of these.

You could get a Boeing on all four of the operators at the time, United had some 720s, although their DC8s shared the operation. American had both 707 and 720, but in their timetables always showed both as 707. The American Convair 990s had pretty much gone by this time, while the TWA Convair 880s were still around, but both these had tended to be used on shorter and less-significant operations.

It's a curious fact that although I've done LAX to Chicago several times eastbound over the years, I've never done so westbound. Yet.