Methyldopa, or Aldomet, has been approved by the Food and Drug Administration and is commonly used to treat high blood pressure. This drug has been approved for several decades and has been shown to be safe and effective. This drug has been identified by the researcher to be able to block the communication between two important types of immune cells; which play a critical role in the autoimmune processes of Type 1 Diabetes. The investigators hypothesize that Methyldopa, over a 6 week treatment period, will block this communication and possibly slow down the destruction of insulin producing cells. The investigators hope to assess the appropriate and safe dose to achieve this effect, along with the drug's ability to maintain insulin production and blood glucose control.