This phase III trial compares adding a new anti-cancer drug (venetoclax) to the usual treatment (ibrutinib plus obinutuzumab) in older patients with chronic lymphocytic leukemia who have not received previous treatment. The addition of venetoclax to the usual treatment might prevent chronic lymphocytic leukemia from returning. This trial also will investigate whether patients who receive ibrutinib plus obinutuzumab plus venetoclax and have no detectable chronic lymphocytic leukemia after 1 year of treatment, can stop taking ibrutinib. Ibrutinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Immunotherapy with obinutuzumab may induce changes in body's immune system and may interfere with the ability of cancer cells to grow and spread. Drugs used in chemotherapy, such as venetoclax work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving ibrutinib and obinutuzumab with venetoclax may work better at treating chronic lymphocytic leukemia compared to ibrutinib and obinutuzumab.