This phase III trial studies how well ibrutinib and obinutuzumab with or without venetoclax work in treating older patients with untreated chronic lymphocytic leukemia. 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.