Place the chicken breast in a shallow sauté pan and add 4 tablespoons water. Cover tightly and poach the chicken for 11-13 minutes on medium heat until the chicken is tender, but cooked through completely and no pink remains. Remove and let stand in the poaching liquid to cool. Remove any visible fat and cut into 2-inch pieces.
Place the chicken and remaining liquid into the blender jar. Add the green beans, salt and butter. Pulse until chunky-smooth or to your child's preference. Store in the refrigerator in single, meal-sized plastic containers. Seal tightly. Warm in the microwave oven before serving. After serving, discard any uneaten portion.