Place sun-dried tomatoes in a bowl. Bring balsamic vinegar, sugar, and 3 tablespoons water to a boil. Pour over tomatoes; let stand 10 minutes. Drain and slice.
Cook pasta according to package directions; reserve 1/2 cup cooking water and drain.
Heat oil in a nonstick skillet over medium heat. Add mushrooms. Cook 1 minute without stirring, then cook, stirring, 5 minutes or until browned. Add garlic; cook 1 minute. Add basil and reserved tomatoes; cook 1 minute. Add tomato sauce; bring to a simmer. Add pasta, 1/2 cup grated Parmesan, reserved cooking water, chicken; toss, and transfer to serving bowl. Add arugula, pine nuts, and remaining Parmesan. Serve.