Afro-Americans tend to have coarser facial hair, and sometimes use special shaving tools to address this issue. "Nigger chin" is an offensive term for non-afro-americans who have similar, coarse, facial hair.
Bryan: "Man, my chin is killing me. It hurts when I shave it and makes me want to eat chitterlings."

Normal Person: "Yeah, you're a nigger chin."
by jgoggogo April 19, 2009
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