Combine the chicken, broth, onion, 1 celery rib, 1 carrot, garlic, salt and black pepper and bring to a gentle simmer.
Cook partially covered for 35 to 40 minutes until the chicken reaches 165°F and pulls easily from the bone.
Remove the chicken, strain the broth and discard the spent vegetables.
Dice the remaining celery and carrots and simmer them in the strained broth with thyme for 10 minutes.
Shred the chicken, add it with the egg noodles and simmer for 8 to 10 minutes until tender.
Return the soup to 165°F and adjust the broth with up to 1 cup hot water if needed.