Bring large pot of salted water to boil. Add pasta and cook according to package directions.
Put olive oil, basil, garlic and spinach leaves (torn in half, if large) in large, shallow pasta dish; toss until mixed.
Drain cooked pasta, retaining ½ cup pasta cooking liquid. Immediately add pasta to olive oil mixture; toss well. Add reserved pasta cooking liquid toss well again.
Add smoked chicken, tomato, vinegar and red pepper flakes; toss until well mixed. Add salt to taste. Serve hot, and top with grated Parmesan cheese.