This is an open-label, pilot study , to determine if Exendin-(9-39), an antagonist of the glucagon-like peptide-1 (GLP-1) receptor with effects on the pancreatic beta cells, increases fasting blood glucose levels in subjects with congenital hyperinsulinism. Our overall hypothesis is that abnormal GLP-1 secretion resulting from dysfunctional nutrient sensing in intestinal L-cells plays a role in the dysregulated insulin secretion characteristic of this disorder, and that antagonism of the GLP-1 receptor will increase fasting blood glucose levels.