Combine first 5 ingredients and 2 tablespoons oil in a large zip-top plastic bag; seal and shake to blend. Add chicken to bag; seal, turning to coat. Refrigerate 1 hour.
Preheat oven to 375°.
Heat a large ovenproof skillet over medium-high heat. Add remaining 1 tablespoon oil; swirl to coat. Remove chicken from bag, draining well and reserving marinade. Add chicken to pan; cook 2 minutes or until browned. Turn chicken over. Place skillet in oven; bake at 375° for 15 minutes or until a thermometer registers 160°. Remove chicken from pan; let stand 5 minutes.
While chicken cooks, pour reserved marinade into a medium saucepan. Add chicken broth and next 3 ingredients (through capers). Bring to a boil; reduce heat and simmer, uncovered, 2 minutes or until sauce is reduced to about 3/4 cup. Remove from heat; stir in basil.
Place 1 chicken breast on each of 4 plates. Drizzle evenly with sauce, and sprinkle evenly with pine nuts.
Tip: This is one of those recipes where you need to have all your ingredients prepped and ready so you're not running around at the end.