Place each chicken breast between 2 sheets of heavy-duty plastic wrap.
Spread flour into a wide, dish. Press chicken into flour to coat completely.
Melt butter with olive oil in a large skillet over medium-high heat; cook chicken in hot butter mixture until no longer pink in the center and the juices run clear, 4 to 5 minutes per side. Remove chicken from skillet to a serving platter and cover with a lid to keep warm.
Pour white wine, lemon juice, capers, and garlic into the pan. Bring the liquid to a boil while scraping the browned bits of food from the bottom of the pan with a wooden spoon; cook at a boil until slightly thickened, about 2 minutes. Season the mixture with salt.
Drizzle sauce over and around the chicken.
4 (6 ounce) skinless, boneless chicken breast halves
1/4 cup all-purpose flour
1 tablespoon butter
1 tablespoon olive oil
1/2 cup white wine
1/4 cup fresh lemon juice
2 tablespoons capers
2 teaspoons minced garlic
1/4 teaspoon salt
1/4 teaspoon freshly ground blac