Jaw
late Middle English: from Old French joe ‘cheek, jaw’, of unknown origin.
wiktionary
From Middle English jawe, jowe, geowe, alteration of *chawe (in early Modern English chawe, chaw), from Proto-Germanic *kawǭ (compare Middle Dutch kauwe(“fish jaw”), kouwe(“mouth cavity”), dialectal German Käu, Keu(“jaw, donkey jowl”)), gradation-variant of *kewǭ (compare Old English ċīan (pl.) ‘gills’, West Frisian kiuw(“gill”), Dutch kieuw(“gill”)), noun from Proto-Germanic *kewwaną (compare English chew). More at chew. Alteration probably influenced by Middle English jolle, chaul(“jowl”), which it replaced (see jowl).
Uncertain, see Jew's harp for more.
etymonline
jaw (n.)
late 14c., jowe, joue, "the bones of the mouth," "A word of difficult etymology" [OED]. Probably from Old French joue "cheek," originally jode, from Gallo-Romance *gauta or directly from Gaulish *gabata, but there are phonetic problems; or perhaps a variant of Germanic words related to chew (v.); compare also the two nouns jowl. Replaced Old English ceace, ceafl. Jaws as "holding and gripping part of an appliance" is from mid-15c.; figuratively, of time, death, defeat, etc., from 1560s.
jaw (v.)
1610s, "to catch in the jaws, devour," from jaw (n.). In slang from 1748, "to gossip, to speak;" 1810 as "to scold." Related: Jawed; jawing. Hence 19c. U.S. slang jawsmith "talkative person; loud-mouthed demagogue" (1887), nautical slang jaw-tackle "the mouth" (1829), and the back-formed colloquial noun jaw "rude talk, abusive clamor" (1748).