1699, sailors' partial translation of Chinese k'wai tse "fast ones" or "nimble boys," first element from pidgin Eng. chop, from Cantonese kap "urgent." Chopsticks, the two-fingered piano exercise, is first attested 1893, probably from the resemblance of the fingers to chopsticks.
to explain more clearly: english sailors heard the cantonese word "kap" (fast), and spoke it as "chop," a chinese-english pidgin word. i don't know if they learned this word on its own and then applied it to "chopsticks," or they learned it through "chopsticks" first.
even now, one occasionally hears someone say "chop chop!" to mean "hurry up." well, ok, i am not sure when i have heard that said -- but somewhere. . .hm, was it "flower drum song," the musical from the 50s? Anyway, it entered my brain somewhere, somehow.