Halve chicken fillets horizontally with a sharp knife and flatten them slightly between sheets of plastic wrap. Sprinkle chicken with salt and pepper to taste. Dust with flour, shaking off excess.
Heat 1 Tbsp. Olive Oil in skillet over medium-high heat. Add half the breast fillets and sauté 2 to 3 minutes on each side until golden brown and cooked through. Remove chicken and set aside. Repeat with 1 Tbsp. olive oil and remaining breast fillets.
Add remaining 1 Tbsp. of olive oil, garlic and mushrooms to skillet and sauté until mushrooms are browned. Add chicken broth and wine. Heat to boiling, scraping to loosen browned bits. Simmer 2 minutes. Stir in lemon juice, butter and capers.
Return cooked breast fillets to skillet. Heat through, turning to coat with sauce.