Place tomatoes in a small bowl. Add enough boiling water to cover the tomatoes. Let stand for 10 minutes. Drain and pat dry; set aside.
Meanwhile, using a sharp knife, cut a pocket in each chicken breast by cutting horizontally through the thickest part to, but not through, the opposite side. Set aside.
In a small bowl combine the feta cheese, cream cheese, basil, and tomatoes. Spoon about 1 rounded tablespoon into the pocket in each chicken breast. Sprinkle the chicken with black pepper.
In a large nonstick skillet, heat oil over medium-high heat. Cook chicken in the hot oil for 12-14 minutes or until no pink remains, turning once. Reduce heat to medium if chicken is browning too quickly. Serve chicken with salad greens. Drizzle with vinaigrette dressing.