In a large cast-iron or nonstick skillet, heat the tablespoon of olive oil over medium heat. Add the chicken and saute until it is browned on all sides and just cooked through (about 7-10 minutes). Remove chicken and place on a plate.
Add the teaspoons of olive oil and the onions to the pan, and cook for 2 minutes. Add the garlic and cook for another minute. Add the tomatoes olives, oregano and basil and cook the sauce for 5-8 more minutes.
Add the chicken and cook until it is heated through.
Put the chicken on plates (over rice if desired), and spoon the sauce equally over the chicken.