1. Pat chicken dry and season with salt and black pepper.
2. Heat oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then brown chicken, turning once, about 6 minutes total.
3. (Chicken will not be cooked through.) Transfer with tongs to a plate.
4. Add garlic, tomatoes, and red pepper flakes to skillet and sauté, stirring, until garlic is pale golden, about 1 minute.
5. Add wine and boil, stirring and scraping up brown bits, until reduced by half, about 1 minute.
6. Add chicken broth and bring to a boil, covered.
7. Add chicken to skillet with any juices accumulated on plate and simmer, covered, until just cooked through, 3 minutes approximately.
8. Transfer chicken with tongs to a platter and keep warm, loosely covered with foil.
9. Stir cream and 2 tablespoons basil into sauce in skillet and bring just to a simmer.
10. Season with salt and pepper.
11. Serve sauce over chicken and sprinkle with remaining 2 tablespoons basil.