Inclusion criteria:

          -  Must have a confirmed diagnosis of Chronic Lymphomcytic Leukemia or Small Lymphocytic
             Lymphoma as per IW-CLL 2008 criteria and require therapy based on meeting at least one
             of the following criteria:

               -  Evidence of progressive marrow failure with anemia (hemoglobin <11.0 g/L) and/or
                  thrombocytopenia (platelets <100 x 10^9/L)

               -  Massive (≥6 cm below the left costal margin), progressive, or symptomatic
                  splenomegaly

               -  Massive nodes (at least 10 cm longest diameter), progressive, or symptomatic
                  lymphadenopathy

               -  Progressive lymphocytosis with an increase of more than 50% over a 2-month period
                  or LDT of <6 months.

               -  Autoimmune anemia and/or thrombocytopenia that is poorly responsive to
                  corticosteroids

               -  Constitutional symptoms, defined as 1 or more of the following:

                    -  unintentional weight loss >10% within 6 months prior to screening

                    -  significant fatigue (inability to work or perform usual activities) fevers
                       >100.5° F or 38.0° C for 2 or more weeks prior to screening without evidence
                       of infection

                    -  night sweats for more than 1 month prior to screening without evidence of
                       infection

          -  Relapsed after or refractory to at least one prior Chronic Lymphomcytic
             Leukemia-directed therapy

          -  Age greater than or equal to 18 years

          -  ECOG Performance Status <2

          -  Heme criteria at screening, unless significant bone marrow involvement of Chronic
             Lymphomcytic Leukemia confirmed on biopsy:

               -  Absolute Neutrophil Count (ANC) ≥500 cells/mm3 (0.5 x 10^9/L). Growth factor
                  allowed to achieve

               -  Platelet count ≥25,000 cells/mm3 (25 x 10^9/L) independent of transfusion within
                  7 days of screening

          -  Adequate hepatic function defined as: AST and ALT ≤ 4.0 x upper limit of normal (ULN),
             bilirubin ≤2.0 x upper limit of normal (ULN) unless bilirubin rise is due to Gilbert's
             syndrome)

          -  Adequate renal function defined by serum creatinine <2.0 x upper limit of normal (ULN)
             unless due to biopsy proven Chronic Lymphomcytic Leukemia kidney infiltration

          -  Women of child-bearing potential and men must agree to use adequate contraception

          -  Patients who have undergone prior allo transplant are eligible provided that their
             transplant day 0 is > 6 months from their first dose of study drug

        Exclusion Criteria:

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

          -  Prior treatment with either obinutuzumab or ibrutinib

          -  History of other malignancies, except:

               -  Malignancy treated with curative intent and with no known active disease present
                  for ≥3 years before the first dose of study drug and felt to be at low risk for
                  recurrence by treating physician.

               -  Adequately treated non-melanoma skin cancer or lentigo maligna without evidence
                  of disease.

               -  Adequately treated carcinoma in situ without evidence of disease.

               -  Low-risk prostate cancer on active surveillance

          -  Concurrent systemic immunosuppressant therapy (eg, cyclosporine A, tacrolimus, etc.,
             or chronic administration of >20 mg/day of prednisone) within 28 days of the first
             dose of study drug.

          -  Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug.

          -  Recent infection requiring systemic treatment that was completed ≤7 days before the
             first dose of study drug.

          -  Known bleeding disorders or hemophilia.

          -  History of stroke or intracranial hemorrhage within 6 months prior to enrollment.

          -  Known history of HIV or active hepatitis C virus (HCV) or hepatitis B virus (HBV).

          -  Any uncontrolled active systemic infection.

          -  Major surgery within 4 weeks of first dose of study drug.

          -  Currently active, clinically significant cardiovascular disease, such as uncontrolled
             arrhythmia or Class 3 or 4 CHF as defined by the NYHA Functional Classification; or a
             history of Myocardial Infarction, unstable angina, or acute coronary syndrome within 6
             months prior to randomization.

          -  Lactating or pregnant.

          -  Patients receiving any other study agents

          -  Patients with known Central Nervous System involvement

          -  Baseline QT Interval Corrected by the Fridericia Correction Formula (QTcF) >480 ms
             unless Left Bundle Branch Block

          -  Patients who require warfarin or other vitamin K antagonists for anticoagulation

          -  Concurrent administration of strong inhibitors or inducers of CYP3A