This Phase 2 study will be the first time that idelalisib is administered to previously untreated patients with hematologic malignancies. Idelalisib has demonstrated clinical activity as a single agent in relapsed or refractory CLL and SLL with acceptable toxicity, which supports its evaluation in previously untreated patients. The study population is limited to patients over 65 years of age because younger patients are generally appropriate for standard immunochemotherapy regimens that are highly active. Since the mechanism of action of idelalisib is distinct from rituximab, it is hypothesized that the combination will be more active than either agent alone. This study will establish initial safety and clinical activity of idelalisib in combination with rituximab in patients with CLL or SLL. Cohort 2 of this study will establish safety and clinical activity of idelalisib alone in subjects with untreated CLL or SLL.