Atezolizumab/Bevacizumab Followed by On-demand TACE or Initial Synchronous Treatment With TACE and Atezolizumab/Bevacizumab

This study is comparing two treatment sequences for liver cancer (hepatocellular carcinoma, or HCC) that cannot be surgically removed: starting with a combination of immunotherapy drugs (atezolizumab and bevacizumab) followed by a procedure that blocks blood supply to tumors (TACE), versus starting with TACE and adding immunotherapy when needed. **You may be eligible if...** - You are 18 or older - You have a confirmed diagnosis of liver cancer (HCC) - Your liver cancer cannot be cured with surgery or ablation - You are eligible for the TACE procedure - Your liver function is relatively preserved (Child-Pugh class A or B7) - You have not received prior treatment for liver cancer - Your HIV test is negative **You may NOT be eligible if...** - Your liver cancer has spread outside the liver or has grown into blood vessels - You have clinically significant fluid buildup in the abdomen (ascites) - You have had prior treatment for liver cancer (including prior TACE) - You have a history of autoimmune disease - You have had a liver or organ transplant - You are on a liver transplant waiting list Talk to your doctor to see if this trial is right for you.