BRING water, vegetables, chives and seasonings to boil in medium saucepan on high heat. Reduce heat to low; cover. Simmer 10 minutes. Do not drain.
MELT butter in large saucepan on low heat. Stir in flour. Cook 2 minutes or until bubbly. Gradually add milk, stirring until well blended. Cook on medium heat until mixture boils and thickens, stirring constantly. Add cheese; cook until melted, stirring constantly.
ADD vegetable mixture; cook until heated through. Do not boil.