Step 1

Preheat oven to 425°F. Stir together tomatoes, vinegar, 1 tablespoon of the oil, and ¼ teaspoon each of the salt and pepper in a small bowl. Let stand at room temperature until ready to use.

Step 2

Toss together corn pieces, green beans, 1 teaspoon of the oil, and ½ teaspoon of the salt on an 18- x 13-inch rimmed baking sheet, and spread mixture in an even layer. Bake in preheated oven 10 minutes. Remove from oven.

Step 3

While corn mixture bakes, sprinkle chicken evenly with 1 teaspoon of the salt and ¼ teaspoon of the pepper. Heat 1 ½ teaspoons of the oil in a large skillet over medium-high. Add 2 of the chicken breasts to skillet. Cook, undisturbed, until browned on bottoms, about 4 minutes. Transfer chicken to a plate. Repeat process with remaining 1 ½ teaspoons oil and chicken.

Step 4

Push corn mixture to 1 long side of baking sheet. Arrange chicken, browned side up, along other long edge of baking sheet. Sprinkle chicken evenly with lemon zest; top each breast with 1 cheese slice. Return baking sheet to oven, and bake at 425°F until a thermometer inserted into thickest portion of chicken registers 160°F, 8 to 10 minutes.

Step 5

Meanwhile, stir together butter, garlic, ¼ cup of the herbs, and remaining ¼ teaspoon each salt and pepper in a bowl.

Step 6

Remove corn from baking sheet, and spread evenly with 2 tablespoons butter mixture. Toss together green beans and remaining 2 tablespoons butter mixture on baking sheet. Stir remaining 2 tablespoons mixed herbs into tomato mixture in bowl; spoon over chicken on baking sheet. Divide chicken, tomatoes, green beans, and corn evenly among 4 plates, or transfer to a large platter.