Inclusion criteria:
* Must have a confirmed diagnosis of Chronic Lymphocytic 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 Lymphocytic 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 Lymphocytic 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 Lymphocytic 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
