Inclusion Criteria:

- Chronic Lymphocytic Leukemia

- Circulating lymphocytes above a specific level

- Circulating lymphocytes showing certain markers

Exclusion Criteria:

- Previous treatment with rituximab or alemtuzumab within 6 months prior to enrollment
in study.

- Previous stem cell transplantation.

- Received any of the following treatments within 4 weeks prior to entering this trial:
A) Anti-cancer therapy, B) Glucocorticoids unless less than 10 mg per day, C)
Radiotherapy.

- HIV positivity.

- Hepatitis B or hepatitis C.

- Other cancerous diseases, except certain skin cancers and cervix cancer.

- Certain serious medical conditions, including kidney or liver disease, some
psychiatric illnesses, and stomach, heart, hormonal, nerve or blood diseases.

- Participation in another trial with a different new drug 4 weeks prior to enrollment
in study.

- Current participation in any other clinical study.

- Pregnant or breast-feeding women.

- Women of childbearing age who are unable or unwilling to use adequate contraception.