In a small saucepan, cook chicken breast half in enough boiling water to cover for 15 minutes or until chicken is no longer pink (internal temperature should be 170°F). Remove from saucepan; cool. Reserve the water the chicken was cooked in. Cut up cooked chicken into small pieces
Meanwhile, grind apple in a food mill or mini food processor with the apple juice until the consistency of applesauce; set aside.
Grind chicken in a food mill or mini food processor. Mix ground chicken and applesauce together. Add 2 to 4 tablespoons reserved cooking liquid for the consistency your child likes. Use within 1 day, or freeze up to 1 month.
Spoon finished food into ice cube trays. Cover with waxed paper and freeze until firm. When ice cubes are frozen, remove cubes from tray and store in a resealable plastic freezer bag or freezer container. Label package with contents and date. Use within 1 month. Before serving, let thaw in the refrigerator overnight.
Heat thawed mixture to lukewarm in a small dish set in a pan of hot water. Stir before serving. Always sample a small bite to make sure the food is not too hot.