Preheat oven to 200°F. Heat 3 tablespoons oil in large skillet over high heat. Sprinkle chicken with salt and pepper. Working in 2 batches, add chicken to skillet. Cook until brown and just cooked through, about 3 minutes per side. Transfer to ovenproof plate and place in oven to keep warm. Discard oil from skillet. Add 3 tablespoons oil to same skillet over high heat. Add mushrooms; saute until wilted and beginning to brown, about 3 minutes. Add broth; boil until almost all liquid evaporates, about 5 minutes. Add olives, plum tomatoes, garlic, shallot, and capers. Sprinkle with salt and pepper. Reduce heat to medium and simmer until liquid is reduced by half, about 7 minutes. Add butter; stir until melted. Mix in teardrop tomatoes. Season to taste with salt and pepper. Spoon mushroom mixture over chicken. Sprinkle parsley and pine nuts over. Garnish with caper berries, if desired, and serve.