Grilled Naan Pizza with Strawberry, Chicken, and Avocado

plus 2 tablespoons balsamic vinegar, divided

medium boneless, skinless chicken breast (about 8 ounces)

extra-virgin olive oil, divided

medium avocado

fresh strawberries (about 1 1/2 cups sliced)

goat cheese (about 3/4 cup crumbled)*

loosely packed fresh basil leaves

cooked naan flatbreads (regular or whole wheat)