I had something similar to this in a restaurant once. It was good, but of course I think this version is way better, mostly because I get to put in as much garlic and basil as I want — which means it has to be delicious. I may not be nice to talk to afterward, but at least I know I am vampire-safe.
Preheat a grill/barbecue or grill pan on high heat. Season the chicken with salt and pepper and put it on the grill/barbecue. Cook for 5 minutes on each side, or until cooked through. Let stand for 5 minutes and then cut each chicken breast into slices ¼-inch thick. Keep warm. Bring a large saucepan of salted water to a boil. Add the pasta and cook, stirring occasionally, for 6 minutes, or until al dente. Drain the pasta and keep warm.
Combine the tomatoes, basil, garlic, and olive oil in a bowl and season with salt and pepper. Divide the chicken among 4 plates and top with some of the pasta. Scatter the tomato mixture over the pasta. Drizzle the vinegar over the tomatoes and sprinkle with Parmesan. Serve immediately.