According to my 1960 Santa Fe timetable there were no sections on the San Fransisco Chief.
Well, it's true, not all the way from Richmond to Chicago.
However, there was a grey Valley series car (which included 6 sections) that ran from Houston to Los Angeles via Temple, Brownwood, Sweetwater and Lubbock, and was picked up at Clovis by the San Francisco Chief and set out at Barstow, for the Grand Canyon to finish the trip to Los Angeles. On the eastward trip, the car was set out by the Grand Canyon and switched onto the San Francisco Chief at Barstow and set out at Clovis for the California Special to forward to Houston. This lasted until the end of sleeping car service on the Clovis-Houston train in 1967.