In 4-quart saucepan, bring chicken broth to a boil. Reduce heat and add potatoes, carrots, celery, onion, salt and pepper; simmer, covered, 10 minutes.
Meanwhile, in a medium saucepan, melt butter; add flour and mix well. Gradually stir in milk; cook over low heat until slightly thickened. Stir in cheese and cook until melted. Add cheese mixture and chicken to vegetable mixture. Cook, stirring, over low heat until all ingredients are heated through.