The goal of this clinical research study is to learn if giving a kind of immune cell called natural killer (NK) cells after chemotherapy will improve the response to a stem cell transplant in patients with CML. The safety of this treatment will also be studied.

NK cells may react against leukemia cells, particularly when they are mismatched for certain HLA tissue type proteins. In the lab, the NK cells are separated from the blood using a machine called a CLINIMACs system. This machine uses certain kinds of cells and antibody-coated magnetic beads to separate the NK cells. The drug aldesleukin (interleukin-2, IL-2) is then added to the NK cells to improve their function. The aldesleukin will be washed out of the cell sample before it is given to you.

The NK cells will be donated from a family member who has a certain genetic type in their blood called HLA that partly matches yours. The stem cells you will receive will come from a separate HLA-identical family member or an unrelated donor.

Fludarabine is designed to interfere with the DNA (genetic material) of cancer cells, which may cause the cancer cells to die.

Busulfan is designed to bind to DNA, which may cause cancer cells to die.

Study Drug Administration:

If you are found to be eligible to take part in this study, 6 days before the NK cell infusion, you will be admitted to the hospital and will receive hydration fluids by vein.

Starting 5 days before the NK cell infusion, you will receive fludarabine by vein over 1 hour for 4 days in a row. On the last 2 days, you will receive busulfan by vein over 3 hours. The day before the NK cell infusion, you will "rest" (not receive any drugs).

Starting 3 days before the infusion, you will receive methylprednisolone by vein over 15 minutes and antithymocyte globulin (ATG) by vein over at least 4 hours for 3 days in a row. ATG is given to help reduce the risk of transplant rejection.

On the day of the NK cell infusion, you will receive the NK cells by vein. You will receive Benadryl (diphenhydramine) by vein over 15 minutes before the infusion to help lower the risk of an allergic reaction.

Starting on the day of the NK cell infusion, you will receive aldesleukin as an injection under the skin 1 time a day for 5 days. Aldesleukin is given to help the NK cells survive and multiply.

Starting 5 days after the NK cell infusion, you will receive ATG by vein 1 time a day for 3 days.

The day after the last ATG dose, you will receive the stem cell transplant by vein.

You will also receive tacrolimus and methotrexate to help lower the risk of a reaction called graft vs. host disease (GVHD). GVHD is when the donated immune cells in the transplant react against the body of the person receiving the cells. You will receive tacrolimus by vein as a continuous infusion for about 2 weeks after the stem cell transplant. After that, you will receive tacrolimus by mouth 1 time a day for at least 3 months.

On Days 1, 3, and 6 after the stem cell transplant, you will receive methotrexate by vein over 30 minutes.

You will also receive Neupogen (filgrastim, G-CSF) as an injection under the skin 1 time a day until your blood cell counts are high enough.

Study Tests:

On Day 5 after the NK cell infusion, blood (about 2 tablespoons) will be drawn to check for NK cells.

During the study, blood (about 2 tablespoons) will be drawn 1 time to check for a protein found on NK cells. This blood will be collected during a routine blood draw, if possible, to avoid an additional needle stick. If you have a central venous catheter (CVC), blood will be drawn through the CVC.

You will need to stay in the hospital for about 4 weeks and have blood draws (about 2 teaspoons) for routine tests as often as the doctor thinks is needed during this time. After you leave the hospital, you will continue as an outpatient in the hospital area, which means you will have to stay close enough to be able to come back for any visits for at least 100 days after the transplant.

Length of Study:

You will be taken off study early if the disease gets worse, if intolerable side effects occur, if not enough NK cells can be collected, or if you are unable to follow study directions.

Your participation on the study will be over once you have completed the follow-up phone calls.

Long-Term Follow-Up:

At 1, 3, 6, and 12 months after your transplant:

• You will have a physical exam.
• You will be asked about any side effects you may have had.
• You will be checked for possible reactions to your treatment, including GVHD and graft failure. Graft failure occurs when donor cells may not be able to grow and multiply in your body. If this happens, there will be a high risk of infections and/or bleeding. If the number of white blood cells does not get back to high enough levels within 3 weeks after the transplant, more stem cells may need to be given.
• Blood (about 4 tablespoons) will be drawn for routine tests and to check the level of the infused NK cells, for immune function tests, and to check the status of the disease.
• If the doctor thinks it is needed, you will have a bone marrow aspiration to check the status of the disease.

One (1) time a year for 2 years after your transplant, if you are unable to return for a follow-up visit, the study staff will call you to ask how you are doing. These phone calls should take about 10 minutes.

This is an investigational study. The way the researchers process the NK cells using the CliniMACs device is investigational. The NK cell process is not FDA approved or commercially available. It is currently being used for research purposes only. Fludarabine and busulfan are FDA approved and commercially available to treat CML.

Up to 32 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients who meet the following eligibility criteria are eligible for inclusion in this study. Pediatric team to assess eligibility appropriate for patient age.
2. Age </= 70 years of age.
3. Patients with diagnosis of CML in first chronic phase or accelerated phase with less than 15% blast in the blood and bone marrow at study entry which has failed to respond adequately to imatinib by the consensus criteria of Baccarani et al: a) no hematologic remission at 3 months, b) no cytogenetic response at 6 months, c) no major cytogenetic response at 12 months, d) no complete cytogenetic response or major molecular response at >18 months, or e) loss of a response with increasing cytogenetic or molecular evidence of disease. Or are intolerant to tyrosine kinase inhibitor therapy. Or with second or greater chronic phase (with prior transformation who respond to treatment and have <15% blasts at study entry).
4. Histocompatible stem cell donor: Patients must have an HLA matched related or unrelated donor (HLA A, B, C and DR) willing to donate for allogeneic hematopoietic transplantation.
5. Haploidentical NK cell donor: Patients must have a haploidentical relative with the absence of a KIR-ligand (HLA molecule).
6. Performance status: Zubrod </= 2 or Lansky PS greater or equal to 70%.
7. Cardiac function: left ventricular ejection fraction >/= 40%. No uncontrolled arrhythmias or uncontrolled symptomatic cardiac disease.
8. Pulmonary function: no symptomatic pulmonary disease. forced expiratory volume at one second (FEV1), forced vital capacity (FVC) and diffusion capacity of lung for carbon monoxide (DLCO) >/= 50% of expected, corrected for hemoglobin. For pediatric patients, if unable to perform pulmonary function tests (most children < 7 years of age), pulse oximetry >/= 92% on room air by pulse oximetry.
9. Renal function: Serum creatinine </= 1.8mg/dl or creatinine clearance greater or equal than 40 cc/min. Creatinine for pediatric patients </= 1.5 mg/dl or </= 2 times upper limit of normal for age (whichever is less).
10. Liver function: Bilirubin </= 1.5 mg/dl (unless Gilbert's syndrome), ALT or AST </= 200 IU/ml for adults unless related to underline disease. For pediatric patients conjugated (direct) bilirubin <2x upper limit of normal, ALT or AST <5 times upper limit of normal.No evidence of chronic active hepatitis or cirrhosis. If positive hepatitis serology, discuss with Study Chairman and consider liver biopsy.
11. Patient or patient's legal representative, parent(s) or guardian able to provide written informed consent. Assent as is age appropriate.

Exclusion Criteria:

1. Uncontrolled infection, not responding to appropriate antimicrobial agents after seven days of therapy. The Protocol PI is the final arbiter of eligibility.
2. Pleural/pericardial effusion or ascites estimated to be >1L
3. HIV-positive.
4. Breast feeding or pregnancy. Pregnancy means a positive beta human chorionic gonadotropin (HCG) test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization.
5. Known allergy to mouse proteins
6. Active hepatitis B or C infection.