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1866, American English (popularized c.1870 by a Christy Minstrel song), perhaps a reduplication of hunkey "all right, satisfactory" (1861), from hunk "in a safe position" (1847) New York City slang, from Dutch honk "goal, home," from Middle Dutch honc "place of refuge, hiding place." A theory from 1876, however, traces it to Honcho dori, said to be a street in Yokohama, Japan, where sailors went for diversions of the sort sailors enjoy.
Satisfactory; fine; copacetic: That may be hunky-dory with the jumping and jiving youngsters
[1866+; origin uncertain; hunky was a generalized term of approval by 1861; as to dory, according to one proposal of 1876 it was brought back by sailors from Yokohama, Japan, where Honcho dori is a street where they found their diversions; the term was popularized by a Christy Minstrels song of about 1870]