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.
c. 1200, "an act of chewing," from chew (v.). Meaning "wad of tobacco chewed at one time" is from 1725; as a kind of chewy candy, by 1906.