Bring water to a boil in a Dutch oven. Add chicken and cook until done. Remove chicken from broth to cool, reserving broth in Dutch oven.
Meanwhile, sauté carrots, celery, onion and parsley in butter in a large skillet until tender. Add garlic and cook one minute. Cut chicken into bite-size pieces. Add sautéed vegetables and chicken to reserved broth. Stir in rice and salt and simmer 15 minutes.
Mix together milk and cornstarch; add to soup. Stir until thickened.