Heat 3 tablespoons oil in large skillet over high heat. Sprinkle chicken with salt and pepper. Working in two 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 the skillet.
Add 3 tablespoons oil to same skillet over high heat. Add mushrooms; sauté 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 pear tomatoes. Season with salt and pepper.
Spoon mushroom mixture over chicken breasts. Sprinkle parsley and pine nuts over and serve.
Notes
If you're preparing this recipe as GLUTEN FREE, just make sure to use brands of chicken broth and olives that are known to be GF.