HuMax-CD20 in Chronic Lymphocytic Leukemia

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.