If gluten-free is important to you, make sure you use gluten-free chicken broth. In a large soup pot, melt butter over medium heat. Add onions, celery and garlic. Cook and stir until vegetables begin to soften, about 3 minutes. Add broth, potatoes, thyme, poultry seasoning, salt and pepper. Bring to a boil, then reduce heat to low and simmer, covered, for 10 minutes. Add cream-style corn and peas and carrots. Simmer 5 more minutes. Stir in chopped chicken and mix well. In a measuring cup, whisk together cream and cornstarch until smooth with no lumps. Add to chicken mixture in pot. Increase heat so the chowder comes to a gentle simmer and begins to thicken. Stir often. Add parsley and serve hot.