MELT butter in medium saucepan. Cook celery and onion until onion is tender, but not browned. Stir in flour and cook about one minute. Whisk in chicken broth, cooking until thickened and bubbly.
REMOVE from heat. Puree mixture in batches, in a blender, until smooth. Return to saucepan.
ADD the peanut butter and milk, stirring to blend thoroughly. Heat through, but do not boil. Serve hot or cold. Garnish with snipped chives and chopped peanuts, if desired.