This phase II trial studies how stopping tyrosine kinase inhibitors will affect treatment-free remission in patients with chronic myeloid leukemia in chronic phase. When the level of disease is very low, it's called molecular remission. TKIs are a type of medication that help keep this level low. However, after being in molecular remission for a specific amount of time, it may not be necessary to take tyrosine kinase inhibitors. It is not yet known whether stopping tyrosine kinase inhibitors will help patients with chronic myeloid leukemia in chronic phase continue or re-achieve molecular remission.