Use the heel of your hand to flatten chicken into more or less even 1/2-inch thickness. Sprinkle both sides with herbes de Provence and season with salt and pepper. In a large skillet, heat 1 tablespoon oil. Add chicken and saute over medium to medium high heat until well-browned on both sides and almost cooked through, about 5 minutes. Remove to plate, leaving drippings in pan.
Add remaining oil to pan. Add peppers and cook, stirring until they begin to soften and brown, about 3 minutes. Add garlic and cook, stirring, for 1 minute. Add wine, bring to a boil, and cook, stirring up any brown bits, for 30 seconds. Return chicken and any accumulated juices to pan, reduce heat to medium-low, and simmer, partially covered, until chicken is cooked through, about 3 minutes. Add olives and heat through, about 1 minute.