Heat a skillet over medium; add 1 tablespoon oil. Pound out chicken, season with 1/8 teaspoon salt and 1/8 teaspoon pepper and place into skillet. Cook for 10 minutes until no longer pink in the center, flipping over half way through; shred or cut into cubes, and allow to cool.

In a large bowl, mix chicken, chopped kale, lemon juice, remaining salt and pepper, chopped apples, and cheese.

Fill pitas with chicken mixture; serve with sliced cucumbers and cherry tomatoes on the side.