chink (n.1)
"a split, crack," 1530s, with parasitic -k + Middle English chine (and replacing this word) "fissure, narrow valley," from Old English cinu, cine "fissure," related to cinan "to crack, split, gape," common Germanic (compare Old Saxon and Old High German kinan, Gothic uskeinan, German keimen "to germinate;" Middle Dutch kene, Old Saxon kin, German Keim "germ;" ), from PIE root *geie- "to sprout, split open." The connection being in the notion of bursting open.
chink (n.2)
"a Chinaman," 1901, derogatory, perhaps derived somehow from China, or else from chink (n.1) with reference to eye shape.
chink (n.3)
"sharp sound" (especially of coin), 1580s, probably imitative. As a verb from 1580s. Related: Chinked; chinking.