Season the chicken breasts on all sides with salt and pepper and cook them in a large sauté pan on high heat with 1 tablespoon of olive oil until it is browned and cooked throughout. There should be no pink.Roughly chop the chicken and set aside.
Next, add 1 tablespoon of olive oil to a large cast iron pot on medium-high heat and add in the carrots, celery, onion and garlic and cook for 8 to 10 minutes or until tender.
Add in the chopped chicken, rice and chicken stock and simmer over low heat for 20 to 25 minutes or until the rice is cooked.
Finish by whisking in the cream, thyme and salt and pepper.