O.E. ceowan "to bite, chew," from W.Gmc. *keuwjanan, from PIE base *gjeu- "to chew." To chew (someone) out is military slang from World War II. Chewing gum is 1850, Amer.Eng., originally hardened secretions of the spruce tree.
(also chew over) To talk; converse; discuss; jaw: We got together to chew about the election/ Drop up and chew it over(1890s+)
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with chew out
Scold harshly, as in Dad will chew you out for taking the car without permission. Originating in the military, this slangy term began to be used during World War I and soon spread to civilian life. Several vulgar versions, such as
chew someone's ass out, should be avoided in polite speech. Also see eat out, def. 2.