Heat soup pot or dutch oven over medium heat and add 3 tablespoons olive oil. Sauté onions, celery and carrots until tender.
Toss in garlic, mushrooms, thyme leaves in the pot and mix to combine. Stir in 1 tablespoon olive oil and let mushrooms cook until tender.
Add water, rice, bay leaves and salt to the pot and simmer over medium heat for 15-20 minutes or until rice is cooked. Stir the pot occasionally.
Once rice is cooked, take out thigh bone, bay leaves from pot and discard. Stir in chicken, reduce heat to medium low, place cover on pot and simmer for additional 15 minutes, stirring the pot occasionally.
Serve immediately with fresh ground pepper, chopped parsley and lemon wedges.