This phase III trial studies how well ibrutinib and obinutuzumab with or without venetoclax work in treating patients with chronic lymphocytic leukemia. Ibrutinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Immunotherapy with monoclonal antibodies, such as obinutuzumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor 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, obinutuzumab and venetoclax may work better in treating patients with chronic lymphocytic leukemia.