I don't believe paper is or was ever used. The chips in the scan below were made by USPC in 1926. USPC used 2 sheets of cellulous nitrate (aka celluloid). The first (and thinner) sheet was opaque and had the litho printed on it. Completing the sandwich was a thick (about 2 times thicker) clear sheet. This sandwich was then pressed into the chip. Total thickness of a USPC inlay was about 20/1000".

Due to the expense (celluloid was imported from Italy) and flamability of the material, the Burt Company switched to plastic. Chips like the Dunes Sultan roulettes used plastic. Inlays were about 12/1000"

Personally the celluloid chips are much nicer. They age with a certain patina that the plastic inlays can't produce.

Of course Jim Blanchard is the expert. Anything I've said is what I've recalled from converstions with Jim (and my memory is none too good)