Sauté onion, carrots, celery, and garlic in olive oil until softened and aromatic.
Add chicken pieces, water or no-salt broth, bay leaf, thyme, and black pepper.
Bring to a gentle boil, then reduce heat and simmer until the chicken is cooked through.
Remove chicken, shred finely, and return it to the pot for a richer, heartier soup.
Stir in parsley, adjust pepper or herbs to taste, and simmer 10 more minutes for deeper flavor.
Add cooked noodles, rice, or a squeeze of lemon juice if desired before serving warm.