Make a 2-inch incision in the thickest part of each chicken breast.
Combinethe chèvre with half of the herb mixture in a medium-size bowl; stuff the chicken breasts with the cheese mixture. Refrigerate for several hours.
Heat the oven to 350°F. Season both sides of the chicken with salt and pepper. Heat the oil in an ovenproof sauté pan over medium-high heat. Sear the chicken breasts, skin side down, until golden brown and crisp. Turn the chicken pieces over, and finish cooking in the oven, about 7 minutes.
Heat the sweet tomato pickles with 2 tablespoons butter and the remaining herb mixture in a small saucepan over medium-low heat.
Wilt the spinach in the remaining 1 tablespoon butter in a separate sauté or frying pan. When the chicken is done, cut each breast in half on a bias, and serve atop half of the spinach. Spoon the pickled tomato butter sauce over the top, and serve.