This is a food item, consuming it (via right click) will replenish your food and water. This item has some anti-radioactive properties, consuming it will lower your radiation level. It will also provide minor healing.
The Cooked Chicken Breast could be consumed by a player by putting it into their Hotbar and pressing the specified key of 1-6. Players could could also consume it from anywhere in their inventory by hovering their mouse over the item and then clicking on it with their right-mouse button after which they could select the Eat option.