1. In a large pot, heat a bit of oil over medium heat. Add the chopped onion and minced garlic, and sauté until fragrant.
2. Add the chicken pieces to the pot and brown them on all sides.
3. Pour in the chicken broth, and add the sliced carrots, celery, salt, pepper, and thyme. Bring to a boil.
4. Reduce the heat and let the soup simmer for about 30 minutes, or until the chicken is cooked through and the vegetables are tender.
5. If using noodles, add them in the last 10 minutes of cooking.
6. Remove the chicken pieces, shred the meat, and return it to the pot. Discard the bones.
7. Adjust seasoning if needed, and serve hot.