In a stockpot, bring chicken broth to a boil. Reduce to a simmer and add in potatoes, carrots, celery, onion, salt and pepper. Cover and simmer for 15 minutes or until vegetables are tender.
In a saucepan, melt butter and add flour and mix well. Gradually stir in milk; cook over low heat until slightly thickened.
Mix in cheese and cook until melted; add to broth mixture along with chicken. Cook and stir over low heat until heated through. Serves 6-8.