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