This study aims to treat your cancer and closely resembles routine care that would be received regardless of participating on a research study. To participate on the study, you will frequently meet with a member of the study team in addition to your oncology care team. The study involves: • Assessments and tests: Measurement of your height, weight, and vital signs (blood pressure, pulse, and temperature); Complete physical examination, Blood sample collection; pregnancy blood test (if applicable); Electrocardiograms (ECG); An echocardiogram (ECHO), multigated acquisition scan (MUGA) or gated heart pool scan (GHPS) scan to check your heart function; Computerized tomography (CT) scan(s) to assess your CLL disease; bone marrow biopsies • Study medications; questionnaires.