Further to the Mad Magazine Chesterfield parody Cool Beans mentions, there was a second verse:

Only top tobacco, straight grade A,
Gives them butts clean flavor when they're thrown away.
That sun-drenched top tobacco's gonna mean
That each cigarette butt you pick up is clean--
Chesterfind!

The piece featured graphics showing a bum asking some pompous rich guy for a dime, getting pushed aside, and then collapsing into the gutter where the cigarette butt the rich guy just tossed aside catches his eye.