Place ground beef in a large, deep skillet. Cook over medium-high heat until evenly brown. Drain, crumble, and set aside.
Simmer carrots, celery, onion, and broth for about 10 minutes or until soft.
Add rice, mixed vegetables, beef, Velveeta, cheese soup, and milk, and cook until cheese is melted. Do not boil. Add sour cream and chives just before serving.
