Frozen Chicken Leg Quarters Suppliers. A Chicken Leg Quarter is made by cutting a “Rear Poultry Half” in two along the center of the backbone. Two roughly equal parts result. Each will have a Chicken Drumstick and a Chicken Thigh. There will also be some portion of the back, some stomach fat and the tail. Chicken Leg Quarters are one of the most economical meat choices you can make for a family because of the amount of meat and the generally lower price. Chicken Leg Quarters are available all year long.