Pre-heat oven to 350 degrees and cover a baking sheet with foil.
In a medium bowl, combine feta, olives, red onion, sun-dried tomatoes, parsley, lemon juice, ¼ tsp pepper, and oregano.
Place chicken on a cutting board and using a sharp knife, make a deep horizontal slice in each chicken breast. Make sure not to cut all the way through. Rub olive oil over chicken and sprinkle on salt and remaining ¼ tsp pepper.
Stuff each chicken breast with as much of the filling as you want.
Place chicken breasts on prepared baking sheet and bake for 25-30 minutes, until chicken is cooked through and/or registers at 165 degrees on a meat thermometer.