Etymology of "chatterbox"
The OED's first citation is
1774 C. Clive Let. 13 Jan. in D. Garrick Private Corr. (1831) I. 604 But I suppose his father can, for he is a fine chatter-box.
but it's easy to find a couple of antedatings:
1761 C. Morell The History of James Lovegrove, Esq II 95 Hold, hold Chatter-box! To your Buſineſs—
1762 Monthly Review Vol. XXVI 112 a ratting braggadocio, a conceited fop, an eternal chatter-box!
Neither citation sheds any light on the etymology. But I note that prattle-box is obviously formed on the same lines as chatter-box and appears somewhat earlier:
1671 J. Glanvill Disc. H. Stubbe 2 Gross Ignoramusses, Illiterate Fools, Prattle-boxes, Catch-Dotterels,..Tories, Cheats, and poor Devils.
And prattle-basket is even earlier:
1602 N. Breton Mothers Blessing sig. E1 But if she be ilfauour'd, blind, and old, A prattle basket, or an idle slut.
I think these earlier forms provide support for chatter-box being originally understood as "a container full of idle talk".
The OED also shows the first use of chatterbox as being 1774. It suggests ‘perhaps in origin akin to clapdish’, ‘a wooden dish with a lid, formerly carried by lepers, beggars from the lazar-houses, and mendicants generally, to give warning of their approach, and to receive alms.’ It had a secondary meaning, now obsolete, as ‘jocularly used of a talkative mouth.’ I don't think the OED comment means that chatterbox is a phonetic corruption of clapdish, but rather that a chatterbox might once have been something like a clapdish.