A Study Evaluating Atezolizumab and Bevacizumab Plus ADI-PEG 20 in Patients With Locally Advanced / Metastatic Hepatocellular Carcinoma

Inclusion Criteria: 1. Ability to understand and the willingness to sign a written informed consent document for participation in this trial 2. Willingness to sign a written informed consent document to participate in laboratory protocol PA13-0291 for the testing of biomarkers as described in this clinical protocol. 3. ≥ 18 years of age 4. Histologically confirmed HCC (documentation of original biopsy for diagnosis is acceptable if tumor tissue is unavailable) or clinical diagnosis by AASLD (American Association for the Study for Liver Diseases) criteria in cirrhotic subjects (presence of nonrim arterial phase hyperenhancement relative to the liver parenchyma with venous washout for tumors \> 1 cm). For subjects without cirrhosis, histological confirmation is mandatory. The determination of cirrhosis status will ultimately lie in the clinical judgment of the surgical oncologist and medical oncologist involved in the care of the patient. 5. Locally advanced or metastatic disease. 6. Measurable disease defined as a lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) and measures ≥ 15 mm with conventional techniques or ≥ 10 mm with more sensitive techniques such as magnetic resonance imaging (MRI) or spiral computed tomography (CT) scan. 7. Eastern Cooperative Oncology Group performance status (ECOG PS) score ≤ 1. 8. Child-Turcotte-Pugh Score A. 9. Record of treated or absence of esophageal varices by esophagogastroduodenoscopy within 6 months of initiating treatment. 10. Adequate organ and marrow function (as defined below) within 14 days of the first dose of study drug: * Absolute neutrophil count ≥ 1,500/μL * Platelets ≥100,000/μL * Hemoglobin \> 9.0 g/dL (may be transfused or receive epoetin alfa \[e.g., Epogen®\] to maintain or exceed this level) * Total bilirubin ≤ 1.5 x ULN with the following exception: \- Patients with known Gilbert disease: serum bilirubin ≤ 3 x ULN * Estimated creatinine clearance \>40mL/min. * Aspartate transaminase (AST) (SGOT) and/or alanine transaminase (ALT) (SGPT) ≤ 5 X institutional ULN * Documented virology status of hepatitis, as confirmed by screening HBV and HCV tests for patients with active HBV: HBV DNA ≤ 500 IU/mL during screening, initiation of anti-HBV treatment at least 14 days prior to randomization and willingness to continue anti-HBV treatment during the study (per local standard of care: e.g., entecavir) * UA with protein less than 2+ * Serum uric acid ≤10 mg/dL (595 μmol/L) (with or without medication control). 11. Negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of study drug and every 4 weeks while taking atezolizumab and bevacizumab (for women of childbearing potential \[WOCBP\]). 12. Not breastfeeding 13. The effects of ADI-PEG 20 on the developing human fetus are unknown. For this reason, women of child-bearing potential (WOCBP) and men who are sexually active with WOCBP must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and for a total of 12 (women) or 7 (men who are sexually active with WOCBP) months after the completion of API-PEG 20 (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following: * Postmenopausal (no menses in greater than or equal to 12 consecutive months). * History of hysterectomy or bilateral salpingo-oophorectomy. * Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy). * History of bilateral tubal ligation or another surgical sterilization procedure. Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. NOTE: Azoospermic males and WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements. However, WOCBP must still undergo pregnancy testing as described in these sections. Exclusion Criteria: Any of the following criteria will disqualify the patient from participation: 1. Any other malignancy from which the patient has been disease-free for less than 2 years (exceptions: non-melanoma skin cancer or in situ carcinoma of any site are allowed) 2. Fibrolamellar HCC, sarcomatoid HCC, or hepatocellular cholangiocarcinoma 3. Prior systemic therapy, anti-PD-1/PD-L1 or VEGF inhibitor or ADI-PEG 20 therapy. Note: Prior surgery, radiation therapy, or local-regional therapy (ablation or arterial directed therapies) are allowed. 4. Receipt of organ allograft(s) 5. Major surgical procedure, open biopsy, or significant traumatic injury with poorly healed wound within 6 weeks prior to first dose of study drug; or anticipates needing for a major surgical procedure during the course of the study (other than defined by protocol such as the pre-treatment fine needle aspirations or core biopsies) within 7 days prior to first dose of study drug. 6. History of inflammatory bowel disease (including Crohn's disease and ulcerative colitis) or a history of autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[e.g., Wegener's granulomatosis\]). 7. History of testing positive for human immunodeficiency virus or has acquired immunodeficiency syndrome (AIDS). 8. Underlying medical condition, which in the opinion of the Investigator, will make the administration of study drug hazardous or will obscure the interpretation of adverse events, such as a condition associated with frequent diarrhea. 9. Has a known risk factor for bowel perforation including a history of acute diverticulitis, abdominal fistula, gastrointestinal perforation, intra-abdominal abscess, or gastrointestinal obstruction. 10. History of primary brain tumor (excluding meningiomas and other benign lesions), any brain metastases, leptomeningeal disease, seizure disorders not controlled with standard medical therapy, or (within the past year) a history of stroke. 11. History of serious systemic disease, including myocardial infarction or unstable angina within the last 12 months; a history of hypertensive crisis or hypertensive encephalopathy, uncontrolled hypertension (systolic ≥ 150 mmHg and/or diastolic ≥ 100 mmHg at the time of enrollment); New York Heart Association (NYHA) Grade II or greater congestive heart failure, unstable symptomatic arrhythmia requiring medication (patients with chronic atrial arrhythmia, i.e., atrial fibrillation or paroxysmal supraventricular tachycardia are eligible); significant vascular disease or symptomatic peripheral vascular disease. 12. History of other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that might affect the interpretation of the results of the study or render the subject at high risk from treatment complications. 13. History of seizure disorder not related to underlying cancer. 14. Known allergy to pegylated compounds. 15. Known allergy to E. coli drug products (such as granulocyte-macrophage colony stimulating factor). 16. Has had influenza-, hepatitis-, or other vaccines within a month prior to initiation of study drugs. 17. Has had a clinical history of coagulopathy, bleeding diathesis or thrombosis within the past year. 18. Significant pulmonary disease including tuberculosis, pneumonia, pneumonitis, etc. 19. Requires recurrent drainage procedures including pleural effusion, ascites, etc. 20. Surgical procedure within 6 weeks of initiation of study treatment. 21. History of severe allergic/anaphylactic reactions to chimeric or humanized antibodies or fusion proteins. 22. Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab formulation. 23. Known hypersensitivity to bevacizumab. 24. Receipt of investigational agents within 28 days prior to initiation of study treatment. 25. History of severe infection within 4 weeks of initiation of treatment. 26. Receipt of stem cell transplantation, liver transplantation, or solid organ transplantation 27. Serious, non-healing wound, ulcer, or bone fracture. 28. Patient is pregnant (positive pregnancy test) or lactating. 29. Prior orthotropic liver transplantation. 30. Prohibited therapies and/or medications: * Prior anticancer therapy with ADI-PEG 20 or anti-VEGF or anti-PD-1/PD-L1 for HCC. Must not be receiving any concomitant systemic therapy for HCC * Complementary medications (e.g., herbal supplements or traditional Chinese medicines) intended to treat the disease under study unless patients agree to stop the complementary medicines at least 14 days before the first study dose. Such medications are permitted if they are used as supportive care. * Live / attenuated vaccine (e.g., varicella; zoster; yellow fever; rotavirus; oral polio; or and measles, mumps, rubella) within a month prior to initiation of study drug or during treatment. * Any other experimental drug while on this study. * Ongoing anticoagulation therapy (although aspirin is permitted). * total parenteral nutrition. * high dose steroid (e.g., \> 10 mg prednisone daily or equivalent) or other more potent immune suppression medications (e.g., infliximab). 31. Inability to comply with the appointments required in this protocol.