Green’s Dictionary of Slang

(US) a complimentary ticket.

1938		D. Runyon ‘Bred for Battle’ in Runyon on Broadway (1954) 620: A Chinee being a ducket with holes punched in it like old-fashioned Chink money, to show that it is a free ducket.
1979		Maledicta III:2 155: chinee; chinee ducket n [DAS 1935] Complimentary ticket; from the holes punched in such a ticket which consequently resembled some Chinese money.