D&RGW documentation does not seem to refer to the line by the nickname. But the newspapers used the term and all spelled it Chili.
Durango Democrat
March 16, 1906
All available narrow gauge engines are in service there, even one of the Chili Line.
Alamosa Courier
January 22, 1916, Saturday
Yesterday's Santa Fe train was stalled in the snow on the Chili Line and was derailed at Volcano as a result of the flanger backing up on a switch.
Antonito Ledger
February 9 1939, Thursday
During the day Tuesday, a first class storm developed, and the engine with a plow attached, assisted by a bunch of snow shovelers had to go south on the Santa Fe line and help the Chili train which ran into trouble several miles south of town.