Season the chicken breasts with salt and pepper. Using a sharp paring knife, cut a slit in the sides of the chicken breasts, forming a pocket. Be careful not to cut all the way through.
Combine the feta, tomatoes, olives, dill, parsley, scallions and 1 tablespoon olive oil in a bowl. Stir until mixed well. Carefully stuff the chicken breasts with the feta mixture and seal the sides shut with water if necessary. Don’t overfill.
Heat a large skillet over medium-high heat. Add the remaining olive oil and sear each chicken breast until browned. Transfer to a parchment-lined baking sheet. Bake for 12-15 minutes, until chicken is cooked through.
Allow the chicken to rest for 5-10 minutes before slicing and serving.