I think we should keep in mind that a chicken, in the form we currently raise, is not a "natural" animal, so trying to find a "natural" diet for it is a lost cause. Chickens like the ones you keep in your back yard do not exist wild in nature. There once was a wild chicken, thousands of years ago, that lived in the Indus Valley in a hot climate and a very specific ecosystem, and ate whatever was available in that ecosystem. Those times are long gone. The chickens that remain today are domesticated, and any "wild" chickens you might see running around are simply feral domesticated chickens, and they do not survive in the "wild" year-round, in climates that have cold winters (or in remote areas far from human settlements and the food sources they provide). Present day chickens have been bred so heavily for egg and meat production that they have totally different dietary needs compared to truly wild birds. They depend on people to feed them a proper diet. The most natural place for a chicken at this point in their evolution is under the care of a human. Just like so many animals we have domesticated and made dependent on us - like cows and dogs and so many others.
So, for the sake of your chickens' well-being, please reevaluate the meaning of the term "natural", and don't turn down what is best for your chickens just because of a philosophical preference.