Heat olive oil in a large pot over medium heat. Season chicken liberally with salt and pepper, and then add to the pot and sauté until browned (about 3-4 minutes). Remove chicken to a plate and set aside. {SKIP THIS STEP if you're starting with cooked, shredded chicken.}
Add carrots, onion, and celery to the pot. Cook, stirring occasionally, until tender (about 10 minutes). Stir in zucchini, tomatoes, garlic, basil, oregano, thyme, and chicken broth. Increase heat to high and bring to a boil.
Stir in chicken and tortellini; reduce heat, and simmer until tortellini is cooked through (about 5-6 minutes). Add spinach and continue to cook and stir for 1 more minute, or just until the spinach wilts.
Season with salt and pepper, to taste. Garnish with fresh parsley or Parmesan cheese and serve!