Sauté the Aromatics. Heat olive oil in a large pot over medium heat. Add onions, carrots, and celery, cooking for 5 minutes until softened. Stir in the garlic and cook for 30 seconds until fragrant.
Add the Chicken and Broth. Place the chicken breasts or thighs into the pot. Pour in the chicken broth, then add salt, black pepper, thyme, and bay leaf. Stir to combine.
Simmer Until Tender. Bring the soup to a gentle boil, then reduce the heat to low and cover. Let it simmer for 25–30 minutes until the chicken is cooked through and tender.
Shred the Chicken. Remove the cooked chicken from the pot and shred it with two forks. Return it to the soup and stir to combine.
Add Optional Ingredients. If using rice, rinse thoroughly add it now and cook for 15 minutes or until tender. For extra brightness, squeeze in the lemon juice.
Serve and Enjoy. Ladle the hot soup into bowls and garnish with fresh parsley. Serve warm and feel the comforting goodness in every bite.