Drizzle the chicken breasts with olive oil and sprinkle with the ground thyme and some salt and pepper. Put the chicken in a roasting pan and roast until cooked through, about 20 minutes. Set aside.
In a pot over medium heat, melt the butter and saute the celery, carrots, onions and bell peppers for 3 to 4 minutes. Sprinkle with the fresh thyme and turmeric and cook for another 2 minutes. Pour in the chicken broth, cover, bring to a simmer and simmer 30 minutes.
Prepare the rice according to the package instructions; keep warm.
Shred or chop the chicken and add it to the pot with the soup. Simmer for another 15 minutes. Stir in the rice and minced parsley and serve.