Currently, there is no approved medical treatment for preservation of the body's ability to produce insulin in patients with Type 1 Diabetes Mellitus (T1DM), and the progression of the disease can have devastating consequences. Inadequate blood glucose control results in many long term complications including kidney disease, blindness, amputation and nerve damage. In spite of the advances in insulin therapy and subsequent glucose control, patients are required to infuse insulin subcutaneously daily throughout their lives, monitor their diet and blood sugar levels, and deal with life-long uncertainties. The investigational therapy under study in this trial, regulatory T cells (Tregs), offers the hope of stabilizing diabetes. Tregs are a specialized subset of T cells that function to control the immune response. Pre-clinical studies in non-obese diabetic mice have demonstrated that adoptive transfer of Tregs can slow diabetes progression and, in some cases, reverse new onset diabetes. The primary objective of this study is to assess the safety of a single intravenous infusion of Tregs in patients with T1DM. The study will also assess the effect of Tregs on insulin-producing beta cell function as well as other outcomes related to diabetes management. Researchers will isolate Tregs from the patient's own blood using specific T cell surface markers (CD4, CD25, and CD127). This subset of cells is then expanded in the laboratory by co-stimulating with anti-CD3 and anti-CD28 immobilized on magnetic beads, and with the use of growth medium containing human serum and IL-2. Following the 14-day expansion, anti-CD3/anti-CD28 beads will be removed and the Tregs will be concentrated and consolidated. The cells will then be resuspended in sterile infusion solution at the required concentration and infused back into the patient through a standard peripheral intravenous line. Subjects will be observed overnight in the clinical research center for any possible side effects following the infusion. A total of 14 subjects will be enrolled. The study will involve 4 dosing cohorts with 3 or 4 adults in each cohort. Each cohort will receive increasing amounts of Tregs. Subjects will be followed over five years to assess safety of the Treg therapy.