Inclusion Criteria:

          -  Documented cluster of differentiation (CD) 20+ B-CLL according to NCI/IWCLL guideline

          -  Total Cumulative Illness Rating Scale (CIRS) score greater than (>) 6 and/or
             creatinine clearance less than (<) 70 milliliters per minute (mL/min)

          -  Previously untreated chronic lymphocytic leukemia (CLL) requiring treatment according
             to NCI/IWCLL guidelines who warrant treatment if they have any of the
             protocol-specified comorbidities

          -  Life expectancy > 6 months

          -  Adequate hematological function, unless abnormalities are caused by underlying CLL

          -  Agreement to use highly effective contraceptive measures per protocol

        Exclusion Criteria:

          -  Any previous CLL treatment

          -  Documented transformation of CLL to aggressive non-Hodgkin's lymphoma (Richter's
             transformation)

          -  Abnormal laboratory test values, unless abnormalities are caused by underlying CLL

          -  History of progressive multifocal leukoencephalopathy

          -  Previous treatment with tocilizumab for any indication

          -  History of severe allergic or anaphylactic reactions to monoclonal antibody therapy

          -  Known hypersensitivity to any of the study drugs

          -  History of prior malignancy unless the malignancy has been treated with a curative
             intent or is in remission without treatment for at least (>/=) 5 years prior to
             enrollment and with the exception of curatively-treated basal squamous cell carcinoma
             of the skin, low grade in situ carcinoma of the cervix, or low grade early stage
             localized prostate cancer treated surgically with curative intent and or ductal
             carcinoma in situ of the breast treated with lumpectomy alone

          -  Treatment with glucocorticoids at any dose (except topical formulations) during the 2
             weeks prior to the start of Cycle 1 Day 1. Regular treatment with glucocorticoids (> 5
             days duration) is also prohibited during the 4-week screening period

          -  Ongoing treatment with immunosuppressive medications or anti-tumor necrosis factor
             biologic therapies

          -  Evidence of significant, uncontrolled concomitant diseases that could affect
             compliance with this protocol or interpretation of results, including significant
             cardiovascular or pulmonary disease

          -  Known active or history of recurrent bacterial, viral, fungal, mycobacterial,
             parasitic, or other infection (excluding fungal infections of nail beds) requiring
             treatment with intravenous (IV) antibiotics or hospitalization within 4 weeks prior to
             the start of Cycle 1 Day 1

          -  Active tuberculosis (TB) requiring treatment within 3 years prior to baseline or
             latent TB diagnosed during screening that has not been appropriately treated

          -  Vaccination with live or attenuated vaccines within 28 days prior to start of
             treatment

          -  Major surgery (within 4 weeks prior to Cycle 1 Day 1), other than for diagnosis

          -  Positive test results for chronic hepatitis B infection or positivity for hepatitis B
             core antibody

          -  Positive test results for hepatitis C

          -  Known history of human immuno-deficiency virus (HIV) seropositive status

          -  Positive test results for human T-lymphotropic virus 1 (HTLV 1)

          -  Pregnant or lactating women

          -  Participation in another clinical study with drug intervention unless the last dose
             administered was greater than 5 half-lives of the study product prior to study start

          -  Any participant actively taking anti-platelet medication or any participant who is
             fully anticoagulated with warfarin, low-molecular weight heparin or a novel oral
             anticoagulant including dabigatran, rivaroxiban, epixiban, and similar

          -  Previous treatment with B-cell depleting agents

          -  Any inherited bleeding disorder