Heat 12 inch skillet, Dutch oven or casserole with lid. Pour in oil and heat until quite hot. Line pan with a batch of chicken breasts and fry over high heat until golden brown on one side, about 2 1/2 to 3 minutes. Turn over and brown other side. Remove with tongs and continue browning remaining pieces. Set chicken aside.
Reduce heat to medium, put garlic and shallots in pan, and saute until fragrant, about 15 seconds. Add oregano, white wine, salt and pepper and saute uncovered about 4 to 4 1/2 minutes, shaking pan from time to time.Add tomatoes and return chicken to pan, cover and cook about 10 to 15 minutes, or until chicken is done. Taste for seasoning and adjust if necessary.
Scoop chicken out onto a platter and serve with rice or over mashed potatoes.