This study will investigate the use of rituximab to see if it can help lower the number of immune B cells thereby preventing the destruction of any remaining insulin producing beta cells that remain at diagnosis. Rituximab is approved by the Food and Drug Administration (FDA) for the treatment of a condition called B-lymphocyte lymphoma. Its effects on the immune system are well understood through its use in organ transplantation. Research has shown that rituximab might be helpful in treating other conditions caused by T cells and B cells, including type 1 diabetes. The goal of this study is to find out if rituximab can preserve residual insulin secretion and prevent further beta cell destruction in type 1 diabetes.