Preheat broiler. Spread pita chips evenly on a large baking sheet. Top with sliced tomatoes and fresh mozzarella.
Place under broiler until cheese begins to melt and brown slightly (watch carefully - will burn quickly.)
Meanwhile, place balsamic vinegar in a small saucepan over medium low heat. Bring to a simmer and cook for 3-4 minutes, stirring frequently until vinegar begins to thicken and form a syrup. Drizzle over nachos. Sprinkle with basil and kosher salt.