Heat the olive oil in a Dutch oven or other heavy pot over medium high heat. Add leek, carrots and celery and stir until the leek is softened, about 3-5 minutes.Add rice to the pot and stir for another 2 minutes.Pour in chicken broth and bring to a boil. Lower heat to a simmer, cover the pot and cook until the rice is done, about 15 minutes.Stir in chicken and season to taste with salt and pepper. Ladle into bowls, garnish with parsley and serve.