Heat olive oil in a large pot over medium heat. Add carrots, celery, onion, bell peppers, and garlic. Cook for 5 minutes until softened and fragrant.
Pour in chicken broth, add the chicken thighs, and season with salt, pepper, Cajun seasoning, onion powder, rosemary, and thyme. Stir and simmer over medium heat for about 15–20 minutes, or until the chicken is tender.
Reduce the heat to low. Remove the chicken from the pot and stir in the rice. Cover and cook for about 5–7 minutes.
Shred the chicken with a fork, then return it to the pot along with the cream of chicken soup. Stir to combine and simmer for another 15 minutes, or until the rice is fully cooked.
Adjust seasonings as needed. If the soup thickens too much, add more broth or water to reach your desired consistency.