1. Preheat oven to 375ºF. In a medium bowl mix goat cheese, tomatoes, shallot, garlic, and the cut spinach leaves.
2. Using a small sharp knife and working with one chicken breast at a time, cut a 2-inch-long horizontal slit into the thick side of the chicken breast. Move knife back and forth in slit to form a pocket. Divide cheese mixture among chicken pockets. Press edges closed and secure with a toothpick to seal. Sprinkle chicken with salt and pepper.
3. Heat oil in large ovenproof skillet over high heat. Add chicken, skin side down; cook for 2 minutes or until skin is brown. Turn chicken over; transfer skillet to oven. Bake until cooked through (170°F) for about 10 minutes.
4. Meanwhile, in a heavy small saucepan melt butter over medium heat. Remove from heat and stir in lemon juice. Slice chicken and place on a serving plate. Drizzle lemon butter over chicken. Garnish with fresh basil.