1. Season chicken breasts with salt and pepper. Dredge in flour and shake off excess.
2. In a large skillet over medium-high heat, melt 1 tbsp of butter with 1 tbsp of olive oil. When butter and oil start to sizzle, add chicken and cook for 3 minutes. When chicken is browned, flip and cook other side for 3 minutes. Remove and transfer to plate.
3. Into the pan add lemon juice, chicken broth, and capers. Return to stove and bring to boil, scraping up brown bits from the pan for extra flavor.
4. Return all the chicken to the pan and simmer for 5 minutes. Remove chicken to platter. Add remaining 1 tbsp butter to sauce and whisk vigorously. Pour sauce over chicken and garnish with parsley.