Preparation Sprinkle chicken all over with 1 tablespoon salt and let stand. While chicken is standing, bring water, broth, and thyme to a boil in a 4- to 6-quart heavy pot, then add beans and cook, uncovered, until crisp-tender, 3 to 6 minutes. Transfer beans with a slotted spoon to a bowl and toss with 1 tablespoon oil and salt and pepper to taste. Add salted chicken to broth and cook at a bare simmer, uncovered, 6 minutes. Remove pot from heat and let stand, covered, until chicken is cooked through, about 15 minutes . Transfer chicken with tongs to a cutting board and cool, about 5 minutes. While chicken is cooling, stir together tomatoes, olives, oregano, pepper, and remaining 1/4 teaspoon salt and 4 tablespoons oil in a bowl. Holding a knife at a 45-degree angle, cut chicken across the grain into 1-inch-thick slices. Divide green beans among 4 plates, then arrange sliced chicken over beans and top with tomato olive mixture. Cooks' NoteBeans, chicken, and tomato olive mixture can be made 2 hours ahead and chilled separately, covered.
Preparation Sprinkle chicken all over with 1 tablespoon salt and let stand. While chicken is standing, bring water, broth, and thyme to a boil in a 4- to 6-quart heavy pot, then add beans and cook, uncovered, until crisp-tender, 3 to 6 minutes. Transfer beans with a slotted spoon to a bowl and toss with 1 tablespoon oil and salt and pepper to taste. Add salted chicken to broth and cook at a bare simmer, uncovered, 6 minutes. Remove pot from heat and let stand, covered, until chicken is cooked through, about 15 minutes . Transfer chicken with tongs to a cutting board and cool, about 5 minutes. While chicken is cooling, stir together tomatoes, olives, oregano, pepper, and remaining 1/4 teaspoon salt and 4 tablespoons oil in a bowl. Holding a knife at a 45-degree angle, cut chicken across the grain into 1-inch-thick slices. Divide green beans among 4 plates, then arrange sliced chicken over beans and top with tomato olive mixture. Cooks' NoteBeans, chicken, and tomato olive mixture can be made 2 hours ahead and chilled separately, covered.