Season chicken breasts on both sides with salt and pepper.
Heat 2 teaspoons oil in 10-inch skillet over medium-high heat. Add chicken and cook, turning once, until browned. Remove chicken to plate.
Reduce heat to medium. Add 1 tablespoon oil, onion and garlic to skillet; stir and cook until onion browns and begins to soften. Stir in figs, broth, balsamic vinegar and rosemary; simmer 1 minute. Stir in olives and capers. Push tapenade to side of skillet and return chicken and juices to pan.
Simmer gently until chicken is cooked through. Remove chicken to warm serving platter. Stir in parsley and pine nuts. Spoon tapenade over chicken.