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The Chinese have two words for chopsticks. The common one, found in Mandarin, the Wu dialects, Hakka and Cantonese, is kuaı-zi. The other word, appearing in Classical Chinese and the Min dialects, is Zhu.
Chinese etymological works relate that the classical term, zhu, rhymes with the word in the Wu dialects for "becalmed", and therefore superstitious sea-faring folk in that region adopted the word kuar to avoid a taboo word. If this seems far-fetched, it should be noted that such derivations of words in Chinese are commonplace.
It is therefore possible to establish that the concept of “speed" and "chop-stick" are related in Chinese, but not because anyone ever found chopsticks quicker to eat with.
While we do not wish to overturn the folk-etymology (indeed, we have no evidence for doing so), we should like to point out an alternative: seventeenth-century craftsmen used the word "chops" both for "jaws" and "vice" (like the ones you lick). See the OED for evidence on this.
Chopsticks were known to Western writers from c. 1540 (Portuguese), and the English word “chopsticks” appears in 1711 describing Chinese eating habits in an account of trade with India.
Chow
The word, meaning "food", is given in Tong Ting Shue as jaau-jaau. It may be related to the word “chow-chow", meaning "mixed”.
Dr Batalha defines a Macau Patoa word, chau-chau, as a Chinese fried food in a sauce, a mixture of different things, or a muddle. She gives as the origin the Cantonese word chaau, to stir-fry.
It seems clear that two different words existed, one of Indian origin, meaning "mixed condiments" or just “mixed”, and the other meaning "food".
But Tong Ting Shue uses jaau-jaau, employing the Chinese characters for “a cover"; he was clearly not struck by any similarity.