Cook potatoes, carrots, celery, and chopped onion in boiling salted water for 10 to 15 minutes, or until tender. Set aside, and do not drain.
Meanwhile, melt butter in a large saucepan; stir in flour and pepper. Continue to cook and stir for 1 minute. Gradually stir in milk; cook, stirring constantly, until thickened. Stir in cheese and corn. Heat, stirring, until cheese is melted. Add reserved vegetables with liquid; heat through.
Corn chowder recipe serves 8.