When my kids ask for more of something without finishing everything on their plate, I just tell them that they still have food on their plates. I will tell them to finish what they have and then I will give them more chicken (like in your situation). When they do finish everything on their plate, they are too full for seconds. But if they refuse to eat anything else on their plate, then they are really not that hungry. I don't give them seconds of anything until they eat all of their food.