In a 3 quart saucepan over medium-high heat, melt butter or margarine. Add onion and cook until tender, about 5 minutes. Stir in flour and cook until flour has blended with onion mixture.

Add chicken broth and cook, stirring constantly, until mixture is slightly thickened. Add milk and heat just to boiling, stirring constantly.

In covered blender at medium speed, blend about 1/4 of soup mixture at a time until smooth. Return to saucepan and, over medium heat, heat just to boiling. Remove from heat.

With wire whisk or slotted spoon, stir in cheese until melted. If cheese does not melt completely, cook over very low heat about 1 minute, stirring constantly.