Heat cast iron or enamel pot over medium heat and add olive oil. Sauté onions, and carrots until tender.
Add tomatoes and stir, then cover for 5–6 minutes or until tomatoes are tender. Stir in garlic, oregano, and tomato paste and mix until combined. Let the base simmer for 2 minutes.
Add chicken pieces into the pot, then add 2–3 cups of water or until chicken is just covered. Stir in Better Than Bouillon and place fresh thyme sprigs on top. Reduce heat to low and simmer for 15–20 minutes.
Remove thyme sprigs, serve, and garnish with Italian parsley if desired.