Preheat oven to 350°. Spread pecans in a baking pan and bake until golden under skins, about 10 minutes. Let cool, then coarsely chop.
Mound salad greens on four dinner plates. In a small bowl, stir vegetable oil, walnut oil, and vinegar to blend. Set aside.
Sprinkle chicken with salt and pepper. Lay on a lightly oiled barbecue grill over a solid bed of medium-hot coals or medium-high heat on a gas grill (you can hold your hand at grill level only 3 to 4 seconds); close lid on gas grill. Cook chicken, turning occasionally, until meat is no longer pink in center of thickest part (cut to test), about 15 minutes total. Transfer chicken to a cutting board. Remove skin if desired.
Slice chicken across the grain 1/2 inch thick; arrange over greens. Tuck nectarine around chicken. Scatter goat cheese and pecans over the top. Stir dressing; pour over salads. Add salt and pepper to taste.
Nut Oils on Salad: A drizzle of walnut, hazelnut, or almond oil makes a salad dressing--like the one in this salad--rich and interesting. Until recently, though, nut oils have generally been imported and pricey. Now, less expensive oils pressed from Western nuts are joining imports in grocery stores.
Nut oils are good for your heart, as well as your salads. Almond and hazelnut oils are rich in monounsaturated fats, and walnut oil supplies omega-3 fatty acids. Refrigerate nut oils after opening; they turn rancid quickly at room temperature.
Note: Nutritional analysis is per serving without skin.