The goal of this clinical research study is learn if a vaccine that contains the patient's own cancer cell immunoglobulin can shrink or slow the growth of Chronic Lymphocytic Leukemia (CLL). This clinical trial is a dose escalation study in which the safety of this vaccine will be studied. This is a dose escalation study in which each patient will receive vaccine at one dose level. Patients will be injected with a fragment of Deoxyribonucleic acid (DNA) containing the sequence of their own immunoglobulin gene. Patients will be required to have their diagnosis of CLL and stage confirmed prior to initiating vaccination. After vaccination patients will receive clinical and immunologic evaluation, including both humoral and cellular responses. The investigator will be assessing the patient's immune response or whether the patient's body recognizes the DNA vaccine. In addition, side effects and reactions to the vaccine will be evaluated.