"Oh Ching Chong opium, taffy on a stick," first line of chorus of "The Chinee Laundryman," 1880, by Frank Dumont, pub. in Philadelphia by Chas. F. Escher Jr. and sung by Charles Backus of the San Francisco Minstrels.
Sheet music at Levy Sheet Music Collection. Very difficult to read.
The Chinee Laundryman

This puts "Ching Chong" firmly in the 19th century.

It is extremely doubtful that "Chu Chin Chow" contributed anything to the 'Ching Chong' rhymes and songs.
It was based on Ali Baba and the Forty Thieves, by its book composer, Australian Oscar Asche. Two or three (more?) films followed (1923, USA, MGM) and in England. It was a very popular musical in the USA and performed by amateur groups, including students in high school.

It has remained a cult musical, and a DVD is available from House of Opera, with the original music by Norton.