• To characterize the biologic activity in response to vaccination with lethally irradiated autologous CLL cells admixed with GM-562 cells, following reduced intensity allogeneic stem cell transplant [ Time Frame: 2 years ] [ Designated as safety issue: No ]
• to estimate duration of disease response, disease free and overall survival. [ Time Frame: 2 years ] [ Designated as safety issue: No ]

• To characterize the biologic activity in response to vaccination with lethally irradiated autologous CLL cells admixed with GM-562 cells, following reduced intensity allogeneic stem cell transplant
• to estimate duration of disease response, disease free and overall survival.

The purpose of this research study is to assess the safety and immune activity of a vaccine made from the participant's own cancer cells, when administered after a reduced intensity transplant. In recent years, researchers at Dana-Farber Cancer Institute have discovered that vaccines made from a patients's own cancer cells, that have been engineered in the laboratory to produce a protein called GM-CSF, can be effective in stimulating a powerful immune response specific to that cancer.

• This study can be divided into four phases: 1) Screening; 2) Reduced intensity transplant phase; 3) Vaccinations (cycle 1 and cycle 2:each cycle lasts 7 weeks) and 4) Vaccine completion.
• Screening Phase: After signing the consent form, participants will be asked to undergo some screening tests and procedures to find out if they are eligible to participate in the study. These tests and procedures are likely to be part of regular cancer care and may be done even if the patient does not take part in the research study. It is important to note that if insufficient numbers of the participants leukemia cells to generate vaccine were collected on the CLL collection and banking study (DFHCC study #06-200), then they will not be eligible to participate in this study.
• Allogeneic reduced intensity stem cell transplant phase: The transplant phase of the study will begin when the participant is admitted to the hospital to receive chemotherapy and stem cell transplant. The minimum duration of hospitalization for the procedure is approximately 8 days. Undergoing transplant involves the following procedures and treatments: Central intravenous catheter; chemotherapy; medications to prevent graft versus host disease (GVHD); medication to prevent infections; physical exams; blood tests and bone marrow biopsy and aspirate.
• Vaccination Phase: Vaccinations will be given in two cycles, of seven weeks each, that are identical with the exception of when they are administered. Cycle 1 vaccination will begin approximately one month after the stem cells have been infused, provided there is no significant evidence of GVHD. Cycle 2 vaccination will be being approximately one month after discontinuing tacrolimus, provided there is no evidence of severe acute or chronic GVHD. The vaccine will be given 6 times over a period of two months. The participant will receive vaccination shots once weekly for 3 vaccines and then every other week for 3 vaccines.
• Skin biopsies will be done after the first and after the fifth vaccinations. Current status of the participants CLL will be assessed to determine how the disease has responded to transplant and vaccination. These tests include analysis of bone marrow and blood tests.
• Vaccine completion phase: After one cycle of vaccination is completed, the participant will return to the outpatient clinic monthly for check-ups for 6 visits, to monitor the effects of the vaccine.
• Since this trial involves the use of genetically modified cells, it is recommended that participants on this trial undergo annual checkups for at least 20 years, in order to monitor for long term effects of the vaccination treatment.

• Biological: GM-K562 vaccine
• Procedure: stem cell transplantation

Inclusion Criteria:

• Advanced CLL, defined as no response or progressive disease during standard nucleoside analogue based regimen; or, evidence of progressive disease within 24 months of completion of nucleoside analogue regimen; or, intolerance to fludarabine; or, failure to achieve complete remission following salvage regimen.
• no sites of adenopathy > 5cm
• (8/8) HLA matched related or unrelated donor available.
• Must have prior banked tumor, collected by peripheral blood draw, leukapheresis, bone marrow biopsy or by lymph node dissection, per DF/HCC protocol 06-200
• ECOG performance status 0-2

Exclusion Criteria:

• Serum creatinine greater than or equal to 2.0mg/dl
• ALT or AST greater than or equal to 3x ULN
• Total bilirubin greater than or equal to 2.0mg/dl (except for patients with Gilbert's syndrome)
• Cardiac ejection fraction <30%
• HIV infection
• Pregnancy