Green’s Dictionary of Slang

(US) the teeth.

1959		H. Ellison ‘Have Coolth’ in Gentleman Junkie (1961) 129: Baby, you want a mouthful of bloody Chiclets, you keep peppering my good nature.
1972		National Lampoon July 49: You can hand him an earful of patriotism along with that mouthful of bloody Chiclets [HDAS].
1992		N.Y. Times 1 May B11: He’s lucky somebody didn’t grab him during the brawl. He’d be spitting out his Chiclets [HDAS].