In a large saucepan, cook tortellini according to package directions. Meanwhile, in a large bowl, combine the spinach, chicken, onion, cranberries and feta cheese. Drain pasta. Cool for 5 minutes. Add to spinach mixture.
For vinaigrette, in a small bowl, whisk the oil, vinegar, tomato paste, garlic, oregano, salt and pepper. Pour over spinach mixture; gently toss to coat. Sprinkle with Parmesan cheese.