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HEAT oven to 350°F.
CUT 3-inch long pocket in one long side of each chicken breast; set aside. Mix 1/2 cup shredded cheese, Neufchatel and peppers; spoon into chicken pockets, using about 2 Tbsp. for each. Secure with wooden toothpicks, if necessary.
PLACE chicken in single layer in 8-inch square baking dish; top with pesto and remaining shredded cheese.
BAKE 20 to 25 min. or until chicken is done (165°F). Remove and discard toothpicks before serving.