Lay chicken breast flat on the cutting board. Carefully, slide the knife (hold it sideways with blade facing away from you) at the top (wider part) of the chicken breast, in the center, and cut a pocket in the middle. DO NOT slice all the way through the bottom or the sides of the chicken breast. Your ultimate goal is to create a pocket inside the breast with opening at the top. Repeat with all three breasts.
In a small bowl, mix minced sun dried tomatoes, Feta cheese, oil, parsley, salt and pepper. Mix well until evenly combined.
Stuff each chicken breast with equal amount of tomato/feta mixture, making sure it is evenly distributed through the pocket. Lightly press each chicken breast.
Rub each chicken with about a tablespoon of pesto.
Preheat a large cooking pan on medium heat and add vegetable oil. Place stuffed chicken breasts in the pan.
Cook over medium/ medium-low heat until done making sure that both sides get nice and golden (lots of flavor comes from the chicken cooked to golden brown). This could take 20-30 minutes, depending on thickness of the chicken.