Basically, gum is an adult pacifier.
(Other Authors and Sources)
Comment, P. K. Wrigley (1894-1977)
P.K. Wrigley was the son of William Wrigley, Jr., the founder of the chewing gum company. His own son, William Wrigley, used the phrase in a 1988 issue of Forbes, which is what is commonly cited, but there is reference to it being from P. K., in E. Darby The Fortune Builders: Chicago's Famous Families (1986). The phrase also shows up (unattributed) in a 1962 Newsweek article about the company.
Quotations about:
pacifier
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I was a closet pacifier advocate. So were most of my friends. Unknown to our mothers, we owned thirty or forty of those little suckers that were placed strategically around the house so a cry could be silenced in less than thirty seconds. Even though bottles were boiled, rooms disinfected, and germs fought one on one, no one seemed to care where the pacifier had been.