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.