In a large bowl, combine the tomatoes, garlic, fresh basil, olive oil, and balsamic vinegar. Sprinkle with a generous pinch of sea salt and some freshly ground black pepper. Let rest at room temperature for 15 minutes.
Add the cooked pasta, tuna, and Kalamata olives, and toss to combine. Transfer to a serving bowl, sprinkle with chives and Parmesan cheese petals. Serve immediately.
