Insulin treatment often causes the blood glucose levels to fall too low. The body usually responds to low blood glucose levels by releasing hormones which act against the insulin to help correct the low blood glucose levels. However, this hormone response can be altered in people with diabetes. Currently there are no therapeutic agents that can be used to improve the recovery from hypoglycemia (low blood sugar). Naltrexone is a tablet used to help people who are addicted to alcohol or morphine-based drugs to remain drug and alcohol-free but it can also affect the levels of the hormones which are released during hypoglycemia. The aim of this study is to determine whether naltrexone can be used to improve and accelerate the recovery from hypoglycemia in patients with type 1 diabetes.