Heat oven to 375° F. Cut a 2-inch pocket in the thickest part of each chicken-breast half.
In a small bowl, combine the Feta and tapenade, then stuff a quarter of the mixture into each pocket.
In a nonstick skillet, heat 2 tablespoons oil over medium to high heat. Season the chicken with pepper. Add to skillet and cook 2 minutes per side or until brown.
Transfer the chicken to an oven-safe baking dish that has been drizzled with 1 tablespoon oil. Bake for 18 minutes.
When the chicken is 5 minutes from being finished, put the salsa and remaining tablespoon oil in the skillet and heat through.
Add the spinach and cook until slightly wilted. Slice the chicken and serve with a squeeze of lemon juice, capers (if desired), and spinach on the side.