Heat grill to medium-high. Clean the grill and lightly oil. In a medium bowl, whisk together the vinegar, 3 tablespoon oil and ½ teaspoon each salt and pepper; stir in the shallot. Add the corn and grape tomatoes and toss to combine; set aside.
Rub the chicken with the remaining 2 teaspoon olive oil, season with ½ teaspoon salt and ¼ teaspoon pepper, and grill until just cooked through, 4 to 6 minutes per side.
Arrange the chicken, sliced tomatoes and mozzarella on a platter. Spoon the corn mixture and any juices from the bowl over the top, then sprinkle with the basil.
