Many chemotherapy combinations may be used to treat patients with chronic lymphocytic leukemia (CLL). Although there are many options, a single, best option is not agreed upon by most cancer specialists. Bendamustine, a medicine recently approved for use in the United States, has been used in combination with rituximab in previous studies to treat patients whose CLL has returned after previous standard treatments. The purpose of this study is to determine whether bendamustine with rituximab is effective for the initial treatment of CLL for patients aged 65 and older.