In a small bowl combine 2 minced garlic cloves, ¼ cup balsamic vinegar, ¼ teaspoon salt, and ¼ olive oil. Whisk to combine.
Place the chicken in a large baking dish and pour over the marinade. Toss to coat and let marinate in the refrigerator at least 30 minutes or up to 8 hours.
Remove the chicken from the baking dish, discarding the marinade. Grill the chicken over medium heat, flipping once, for 8-12 or until cooked through and no longer pink in the middle.
While the chicken is grilling, combine the tomatoes, avocado, 1 minced garlic clove, shallot, 2 tablespoons balsamic vinegar, 2 tablespoons olive oil, ½ teaspoon salt, basil, and pepper in a medium bowl. Stir gently to combine.
Remove the chicken from the grill. Serve with the salad on top or alongside.