Preheat oven to 400F.
Lay the chicken breast on cutting board and slice in 1/2 as if to make a pocket as when you slice a roll for a sandwich. Do not cut completely through (you will be stuffing the inside of the breast like a sandwich).
Heat the oil in the skillet on low/med. Add the kale/spinach and basil. Stir the vegetables to coat with oil. Cook about 3 minutes or until wilted. Remove from the heat.
Add the cheese to the kale/spinach and stir to combine. Put mixture between the chicken halves.
Secure chicken halves with oiled toothpicks. Brush the top of the chicken with oil (this amount should be small, if you think you are using 1 tsp. make sure it is part of your oil allowance) and sprinkle liberally with black pepper.
Bake for about 20 minutes. Check for doneness (chicken should be all white and have no remaining pink color). Remove toothpicks to serve.