The primary aim of this trial is to generate a preliminary analysis of this novel therapeutic approach and laboratory studies for patients with recurrent or refractory CLL. Further, this pilot trial will demonstrate the feasibility of the translational science methods proposed for this new collaboration of investigators. The investigators hypothesize that patients with relapsed CLL are recruitable to this study, that the methods for measuring simvastatin concentration and target protein translation are feasible, and that the investigators can efficiently apply the laboratory research methods to patient blood samples before and after patients have taken the study medication.