"incessant talker," 1774, from chatter (n.) + box (n.1). Compare saucebox. Other old terms for the same thing include prattle-basket (c. 1600), prate-apace (1630s).
chatoyant
Chattahoochee
Chattanooga
chattel
chatter
chatterbox
chatty
Chaucerian
chauffer
chauffeur
Chautauqua