The purpose of this research study is to see if Dasatinib is effective and safe to give to people with relapsed chronic lymphocytic leukemia (CLL) and to determine the effects of the drug on LYN kinase activity in blood and bone marrow. Recent research shows that a key enzyme in CLL cells is responsible for cell survival. This enzyme is called LYN kinase. Laboratory studies show that inhibition of LYN kinase in CLL cells results in the death to CLL cells. Dasatinib has the ability to inhibit LYN kinase and, therefore, should have some effect on CLL cells.