In a large pot, heat olive oil over medium heat. Add onions, carrots, and celery, then sauté for about 5 minutes until softened. Stir in the minced garlic and cook for another minute.
Pour in the chicken broth and add thyme, parsley, salt, pepper, and the bay leaf. Bring the mixture to a gentle boil.
Reduce the heat to low and stir in the shredded chicken and cooked rice. Let everything simmer for 10–15 minutes to allow the flavors to meld together.
Taste the soup and adjust the seasoning as needed. If desired, squeeze in fresh lemon juice for a bright, fresh flavor. For another comforting meal, check out Chicken Alfredo Casserole!