Trim visible fat from chicken breasts. Remove the tenders (the long thin flaps); reserve for another use. Place trimmed chicken breasts between 2 pieces of plastic wrap. Pound with a rolling pin, meat mallet or heavy skillet until flattened to an even thickness, about 1/2 inch. Combine flour, salt and pepper in a shallow glass dish. Dredge chicken in seasoned flour, shaking off excess. (Discard any leftover flour.)
Heat oil in a large nonstick skillet over medium-high heat. Add chicken and cook until well browned and no longer pink in the center, 4 to 5 minutes per side. Transfer to a plate, cover and keep warm. dd onion, garlic and anchovy paste, if using, to the skillet; cook over medium heat, stirring, for 1 minute. Add broth, wine and tomatoes; bring to a simmer. Cook until slightly thickened, 6 to 7 minutes. Stir in basil and olives. Return the chicken and juices to the pan; reduce heat to low and heat through. Spoon sauce over the chicken.