Preheat the oven to 200 degrees. In a small bowl, combine the rosemary, thyme, garlic and 2 teaspoons salt. Rub all over the chicken.
In a large skillet, heat 2 tablespoons olive oil over medium-high heat. Place 2 chicken breasts, skin side down, in the pan and top with a heavy skillet to flatten. Cook for 7 minutes, turn and fry until cooked through, about 4 minutes. Keep warm on a baking sheet in the oven while you fry the remaining chicken in 2 more tablespoons olive oil.
In a large bowl, whisk together the remaining 2 tablespoons olive oil, the vinegar, shallot, mustard and 1/4 teaspoon salt. Add the spinach and toss; top with the goat cheese and toasted walnuts. Serve with the chicken.