Preheat oven to 400 degree F. Stir goat cheese, tarragon, 1 teaspoon thyme, 1 tablespoon oil, and the zest together in a small bowl; salt and pepper to taste.

Rinse and pat chicken dry. Starting at one end of chicken, gently work your fingers between skin and meat, without tearing, to form a pocket under skin. Spread one-sixth of cheese mixture under skin of each breast. Press top of skin to distribute cheese mixture evenly.

Toss together corn, tomatoes, remaining 1 teaspoon thyme, and 1 tablespoon oil; salt and pepper to taste.

Tear six 15- by 15-inch pieces of parchment paper and spoon about 1 cup corn mixture onto top half of each. Top each with a chicken breast, skin side up. Season with salt and pepper and drizzle with remaining 1 tablespoon oil and the juice. Fold bottom half of paper over to meat top edge. Roll and fold the two edges together toward you to seal, then repeat with sides. Using kitchen string, tie entire packet together like a gift.

Place packets in a shallow baking pan, with chicken skin side down, and roast in middle of oven, 30 minutes. Remove from oven and let stand 5 minutes. Transfer packets to serving plates and allow guests to untie, being careful to avoid hot steam. Makes 6 servings.