Place chicken breasts on a shallow roasting pan or cookie sheet with sides. Pour on about 2 tablespoons olive oil, sprinkle generously with salt and pepper and rub all over both sides of the chicken breasts to coat well. Arrange skin side up and put in the upper part of the oven.
Cut tomatoes in half lengthwise. Cut shallots in half from top to root end, remove outer skin and then slice each half into 4 pieces lengthwise. Place tomatoes and shallots in another roasting pan or cookie sheet. Toss with about 1 tablespoon of oil, salt and pepper. Spread into an even layer. Lay 4 or 5 sprigs of thyme over the tomatoes and shallots. Place in lower part of oven with chicken.
Cook chicken and tomato/shallot mixture for 40 minutes. The chicken should be golden brown and the juices should run clear when pricked with a knife. Tomatoes should be tender and starting to caramelize. Remove thyme sprigs and discard.
Cover chicken with foil and let rest while preparing the beans.
Put beans into a large skillet; add roasted tomatoes and shallots, chicken stock, oregano and some fresh thyme leaves (about 2 teaspoons) pulled from the stems. Cook over medium high heat until tomatoes start breaking apart and chicken stock is almost all reduced. Will likely be about 5 minutes. Taste for seasoning; add more salt and pepper if necessary.
Arrange bean/tomato mixture on a platter and top with chicken breasts. Drizzle with additional olive oil (about 1 tablespoon) and garnish with chopped fresh parsley.