Inclusion:

          1. Patients will have a diagnosis of CLL or SLL or RTand are: a) Cohort 1: Patients with
             treatment naïve CLL/SLL who meet IWCLL criteria for treatment or b) Cohort 2: RT
             (treatment-naïve or R/R)

          2. Age >/= 18 years

          3. Eastern Cooperative Oncology Group (ECOG) Performance Status </= 2

          4. Patients must have adequate renal and hepatic function: -- Serum bilirubin </= 1.5 x
             upper limit of normal (ULN). For patients with Gilbert's disease, serum bilirubin up
             to </= 3 x ULN is allowed provided normal direct bilirubin. -- Serum creatinine </=
             1.5 x ULN, -- Alanine aminotransferace (ALT) and aspartate aminotransferase (AST) </=
             2.5 x ULN

          5. Females of childbearing potential [A woman is considered to be of childbearing
             potential if she is postmenarcheal, has not reached a postmenopausal state (>/=12
             continuous months of amenorrhea with no identified cause other than menopause), and
             has not undergone surgical sterilization (removal of ovaries and/or uterus)] must have
             a negative serum or urine beta human chorionic gonadotrophin (b-hCG) pregnancy test
             result within 14 days prior to the first dose of treatment and must agree to remain
             abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a
             failure rate of <1% per year during the treatment period and for 6 months following
             the last dose of the study drugs. Examples of contraceptive methods with a failure
             rate of <1% per year include bilateral tubal ligation, male sterilization, hormonal
             contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and
             copper intrauterine devices.

          6. #5 Continued - Males who have partners of childbearing potential must agree to use an
             effective contraceptive method such as a barrier method during the study and for 6
             months following the last dose of study drugs. Males should also refrain from donating
             sperm.

          7. For patients receiving therapeutic anticoagulation: stable anticoagulant regimen

          8. Patients or their legally authorized representative must provide written informed
             consent

        Exclusion:

          1. Prior malignancy active within the previous 2 years except for locally curable cancers
             that have been apparently cured, such as basal or squamous cell skin cancer,
             superficial bladder cancer, carcinoma in situ of the cervix or breast, or localized
             prostate cancer. If patients have another malignancy that was diagnosed/treated within
             the last 2 years, such patients may be enrolled if the likelihood of requiring
             systemic therapy for this other malignancy within 2 years is less than 10%, as
             determined by an expert in that particular malignancy at MD Anderson Cancer Center and
             after consultation with the Principal Investigator.

          2. Prior treatment with CTLA-4, PD-1, PD-L1, or CD137 mAb, or venetoclax.

          3. Any major surgery, radiotherapy, chemotherapy, biologic therapy, immunotherapy,
             experimental therapy, investigational therapy within 4 weeks prior to the first dose
             of the study drugs. Note: for patients on oral targeted therapies, a wash-out of 3
             days from cycle 1 day 1 is acceptable.

          4. Adverse events from prior anticancer therapy that have not resolved to Grade </= 1
             except for alopecia

          5. Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias,
             congestive heart failure, or myocardial infarction within 3 months of screening, or
             any Class 3 or 4 cardiac disease as defined by the New York Heart Association
             Functional Classification

          6. History of stroke or cerebral hemorrhage within 3 months

          7. Patients who have uncontrolled hypertension (defined as sustained systolic blood
             pressure >/= 160 mmHg or diastolic >/= 100 mmHg)

          8. Known evidence of active cerebral/meningeal CLL. Patients may have a history of
             central nervous system (CNS) leukemic involvement if definitively treated with prior
             therapy and no evidence of active disease at the time of registration (defined as >/=
             2 consecutive spinal fluid assessments with no evidence of disease)

          9. Active, uncontrolled autoimmune hemolytic anemia or immune thrombocytopenia requiring
             steroid therapy (>10mg/day of prednisone or equivalent).

         10. Active or history of autoimmune disease or immune deficiency, including, but not
             limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus
             erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid
             antibody syndrome, Wegener granulomatosis, Sjögren's syndrome, Guillain-Barré
             syndrome, or multiple sclerosis), with the following exceptions: Patients with a
             history of autoimmune-related hypothyroidism who are on thyroid replacement hormone
             are eligible for the study. Patients with controlled Type 1 diabetes mellitus who are
             on an insulin regimen are eligible for the study. Patients with eczema, psoriasis,
             lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g.,
             patients with psoriatic arthritis are excluded) are eligible for the study provided
             all of following conditions are met:

         11. #10 Continued: a. Rash must cover < 10% of body surface area b. Disease is well
             controlled at baseline and requires only low-potency topical corticosteroids c. No
             occurrence of acute exacerbations of the underlying condition requiring psoralen plus
             ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin
             inhibitors, or high potency or oral corticosteroids within the previous 12 months.

         12. Patients with organ allografts (such as renal transplant) are excluded

         13. Patients who are on high-dose steroids (doses >10mg/day of prednisone or equivalent)
             or immune suppression medications. NOTE: Patients on high-dose steroids (doses
             >10mg/day of prednisone or equivalent) or immune suppression medications are eligible
             provided these drugs are discontinued at least 3 days prior to starting on the study
             drugs

         14. Patients with uncontrolled active infection (viral, bacterial, and fungal) are not
             eligible

         15. History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced),
             organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing
             pneumonia, etc.), or evidence of active pneumonitis on screening chest computed
             tomography (CT) scan. Note: History of radiation pneumonitis in the radiation field
             (fibrosis) is permitted.

         16. Known clinically significant liver disease, including active viral, alcoholic, or
             other hepatitis; cirrhosis; fatty liver; and inherited liver disease

         17. Current or chronic hepatitis B or C infection, or known seropositivity for human
             immunodeficiency virus (HIV)

         18. Patient is pregnant or breast-feeding or intending to become pregnant during the
             course of the study or within 6 months after the last dose of the study drugs.

         19. Known hypersensitivity to Chinese hamster ovary cell products or other recombinant
             human antibodies or fusion proteins.

         20. Patients may not receive other concurrent investigational agent, chemotherapy,
             radiotherapy, or immunotherapy for CLL. NOTE: Localized radiotherapy to an area not
             compromising bone marrow function does not apply

         21. Received strong CYP3A inhibitors or strong CYP3A inducers within 7 days of starting
             venetoclax

         22. Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study
             treatment, or anticipation of need for such a vaccine during the course of the study
             or within 5 months after the last dose of atezolizumab.

         23. Other severe acute or chronic medical or psychiatric condition or laboratory
             abnormality that in the opinion of the investigator may increase the risk associated
             with study participation or investigational product administration or may interfere
             with the interpretation of study results and/or would make the patient inappropriate
             for enrollment into this study