Heat oil i a large pot (Dutch oven).
Add chicken and cook for 1-2 minutes per side, until no longer pink.
Add garlic, onion, carrot and (celery), salt, pepper, oregano and basil Cook for 2-3 minutes, stirring frequently. Add in the rinsed rice and chicken stock. Cook for 25-30 minutes, until the rice is fully cooked.
In a small bowl combine cornstarch and water. Add to the soup. Add the heavy cream. Cook for 2-3 more minutes, stirring frequently.
Add more salt and pepper to taste. Garnish with parsley.