This study is limited to patients with classic congenital adrenal hyperplasia due to 21-hydroxylase deficiency, but has the potential to significantly improve the lives of patients with other forms of adrenal insufficiency. Each of these diseases requires life-long treatment and this novel approach to drug delivery has the potential to significantly improve patients lives. This newly approved pilot study has enrolled one patient and is actively recruiting. In addition, this study will provide information on the safety and tolerability of using a pump to deliver hydrocortisone, and will generate data that will be used in the design of future pediatric studies.