Heat the olive oil in a large pot over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion, carrots, celery, and garlic to the pot. Stir and cook for 4 minutes until the vegetables begin to soften.
Pour in the low-sodium chicken broth and add the brown rice along with the dried thyme. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 40 minutes until the rice is tender and the chicken is cooked through.
Stir in the fresh lemon juice, chopped parsley, and black pepper. Serve the soup warm.