Brief Summary: This phase I/II trial studies the best dose and side effects of gemcitabine and how well it works with clofarabine and busulfan and donor stem cell transplant in treating participants with chronic lymphocytic leukemia. Drugs used in chemotherapy, such as gemcitabine, clofarabine, and busulfan, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving chemotherapy before a donor stem cell transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. The donated stem cells may also replace the patient's immune cells and help destroy any remaining cancer cells.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the maximum tolerated dose (MTD) of gemcitabine when administered with busulfan and clofarabine. II. To estimate the day 100 treatment-related mortality (TRM) for the preparative regimen busulfan, clofarabine, and gemcitabine followed by allogeneic hematopoietic cell transplantation (HCT) for patients with chronic lymphocytic leukemia (CLL). SECONDARY OBJECTIVES: I. To determine the rate of progression-free survival (PFS), graft versus host disease (GVHD), engraftment, and overall survival (OS) for this treatment regimen at one year post treatment completion. OUTLINE: This is a dose-escalation study of gemcitabine. Participants receive gemcitabine intravenously (IV) over 10-25 minutes on days -6 and -4, clofarabine IV over 1 hour and busulfan IV over 3 hours on days -6 to -3. Participants with matched unrelated donors also receive anti-thymocyte globulin IV over 4 hours on days -3 to -1. Starting day -2, participants receive tacrolimus orally (PO) daily for up to 6 months. Participants undergo hematopoietic allogeneic stem cell transplant on day 0, then receive methotrexate IV over 15 minutes on days 1, 3, 6 and 11, and filgrastim subcutaneously (SC) once daily (QD) beginning 1 week after transplant until blood cell levels return to normal. After completion of study treatment, participants are followed up at 3, 6 and 12 months, then every 6 months for 1 year.