CLL cells will be obtained from bone marrow biopsy and blood draws. The genetic material contained in the CLL cells will be examined for the presence of tumor-specific mutations. This information will be used to prepare small protein fragments, which are called "peptides." The vaccine will consist of up to 20 of these peptides as well as a drug called Poly-ICLC. A peptide from the tetanus vaccine will also be included to boost the immune response. Half of the patients, enrolled in the second half of this trial, will also receive low doses of a chemotherapy drug called cyclophosphamide.