"short, thick piece" of something, 1690s, probably a nasalized variant of chuck (n.1) "cut of meat;" meaning "large amount" is 1883, American English. Meaning "person or beast that is small but thick-set and strong" is from 1822.
"to throw," 1835, American English, from chunk (n.) or by similar mutation from chuck (v.1). Related: Chunked; chunking.
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