Preheat oven to 400°F; place rack in the middle of the oven. Line a 15x10x1-inch baking pan with foil; coat the foil with nonstick cooking spray and set aside. In a small bowl mix together 1 tablespoon of the oil, garlic, 1 tablespoon rosemary, vinegar, lemon peel, mustard, 1/4 teaspoon of the salt, and 1/4 teaspoon pepper. Very gently loosen the skin over the breast and legs of chicken. Spoon rosemary mixture over the breast and leg meat and rub in. Place chicken, breast side up, in prepared pan. Drizzle with remaining 1 tablespoon oil and sprinkle with 1/4 teaspoon each salt and pepper.
Roast, uncovered, for 45 minutes or until an instant-read thermometer inserted in breast registers 170°F. Remove and cover with foil; let stand 10 minutes.
Meanwhile, in a medium saucepan combine the nectar, figs, lemon juice, 1/2 teaspoon rosemary, 1/8 teaspoon salt, and 1/8 teaspoon pepper. Bring to boiling over medium-high heat. Boil gently, uncovered, for 2 minutes. Remove from heat and cool 5 minutes. Transfer to a food processor or blender. Cover and process or blend about 10 seconds or until smooth. If necessary, add enough additional nectar to thin to desired consistency.
Cut chicken into 8 pieces. Serve fig sauce with chicken.