Old English ceowan "to bite, gnaw, chew," from West Germanic *keuwwan (source also of Middle Low German keuwen, Dutch kauwen, Old High German kiuwan, German kauen), perhaps from PIE *gyeu- "to chew" (source also of Old Church Slavonic živo "to chew," Lithuanian žiaunos "jaws," Persian javidan "to chew").
Figurative sense of "to think over" is from late 14c.; to chew the rag "discusss some matter" is from 1885, apparently originally British army slang. Related: Chewed; chewing. To chew (someone) out (1948) probably is military slang from World War II. Chewing-gum is by 1843, American English, originally hardened secretions of the spruce tree.
"to chew, chew roughly," 1520s, unexplained phonetic variant of chew (v.). OED notes that 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.
"to chew (food)," 1640s, back-formation from mastication, or else from Late Latin masticatus, past participle of masticare "to chew." Related: Masticated; masticating.
"chew deliberately or continuously," early 15c. variant of mocchen (late 14c.), imitative (with -n- perhaps by influence of crunch), or perhaps from or influenced by Old French mangier "to eat, bite," from Latin manducare "to chew." Related: Munched; munching.
also papier mache, material prepared from paper pulped to a doughy consistence, 1753, from French papier-mâché, literally "chewed paper," from Old French papier "paper" (see paper (n.)) + mâché "compressed, mashed," from past participle of mâcher, literally "to chew," from Late Latin masticare "to chew" (see mastication).