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.
In a medium saucepan, cook the sweet potato, covered, in a small amount of boiling water for 20 to 25 minutes or until very tender. Drain sweet potatoes, reserving cooking liquid. Use a fork or potato masher to thoroughly mash potatoes.
Grind chicken in a food mill or mini food processor. Mix ground chicken and sweet potatoes together. Add 1/2 cup of the reserved cooking liquid or more 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.