Heat oil in a large saucepan over medium heat. Add carrot, celery, and onion; sauté 4 minutes or until tender. Add rice and next 4 ingredients; stir well. Bring to a boil; reduce heat, and simmer, covered, 45 minutes or until rice is tender.
Add peas, and stir gently. Remove from heat, and let stand 5 minutes. Add dill, and stir gently.