According to the Candy Professor, Chicken Dinner Candy Bars were introduced by the Sperry Candy Company of Milwaukee in 1923. They soon became one of the best selling candy bars of their day. Despite the name, they had nothing to do with chicken or dinner. The bar was a chocolate-covered nut roll. (Sounds pretty good!)
Wikipedia claims the name was a reference to President Herbert Hoover's promise of a "chicken in every pot." But that can't be right if the bars were introduced in 1923. The Candy Professor argues that the name was just an advertising gimmick to get people's attention.
Wikipedia also says that early TV commercials for Chicken Dinner Candy had a jingle that went, "Chick - Chick - Chick - Chick - Chicken Dinner" -- in the cadence of a rooster crowing.
The image of the Chicken Candy advertisement comes from an eBay auction. The seller wants $175 for the vintage cardboard advertisement, which seems a lot, though perhaps not if that's the kind of thing you collect.