Preheat oven to 350 degrees F (175 degrees C).

Combine shredded chicken, 1/2 cup pico de gallo, 1/2 cup sour cream, 1/2 cup Mexican cheese blend, and taco seasoning in a large bowl.

Spray a baking dish with cooking spray. Fill each pepper with as much chicken mixture as possible and place in the baking dish. Sprinkle pepper halves with 1/4 cup Mexican cheese blend. Cover with olives and remaining 1/4 cup cheese.

Bake in the preheated oven until cheese is melted and peppers have begun to soften, 15 to 20 minutes. Top each cooked pepper with a dollop of pico de gallo and sour cream.