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1520s, unexplained phonetic variant of chew (v.). OED points out the variant form chow was "very common in 16-17th c." Bartlett's "Dictionary of Americanisms"  says chaw, "Although found in good authors, ... is retained, in this country as in England, only by the illiterate." Related: Chawed; chawing. The noun meaning "that which is chewed" (especially a quid of tobacco) first recorded 1709.