Dasatinib in Relapsed Chronic Lymphocytic Leukemia

* After the screening procedures confirm that the participant is eligible and willing to participate in the research study, they will have the following tests and procedures. * Dasatinib is given orally once daily. Each participant will have a pill diary to record doses and any missed doses. All necessary drug refills will be given during clinic appointments, at which time the pill diary and any unused study drug will be returned. * During the first month of study treatment the participant will come to the clinic at the following intervals: Day 1: An EKG will be performed two hours after the first dose of medication; Days 3-8: Blood samples will be drawn once between days 3-8; Weeks 2-4: A physical examination, EKG and blood samples will be drawn once a week. * Beginning with the second month of study treatment, participants will come to the clinic monthly for up to two years. The following tests and procedures will be done; physical examination (monthly), blood work (monthly), pregnancy test (monthly), EKG (monthly for 6 months, then when medically indicated), CT of the neck, chest and abdomen (every 2 months for 6 months, then once every 6 months), at the end of month 2, additional blood will be drawn for research testing. * Participants can continue to take the study drug for up to two years as long as their disease does not progress and they are not experiencing any serious side effects.