Inclusion Criteria:

        Age ≥ 18 years of age. Relapsed or refractory B-cell CLL or biopsy-proven SLL. Treatment
        required in the opinion of the investigator

        Must have had at least one standard treatment with a regimen containing at least one of the
        following agents/classes of agents; and where specified, must also meet the treatment
        duration, progression, and/or relapse criteria for that class of agent:

          -  Fludarabine

          -  An alkylator (eg, chlorambucil, bendamustine)

          -  A BTK inhibitor (eg, ibrutinib, acalabrutinib); and must have progressed or relapsed >
             6 months after last BTK inhibitor treatment

          -  An anti-CD20 monoclonal antibody (eg, rituximab, obinutuzumab)

          -  A BCL-2-family protein inhibitor (eg, venetoclax, navitoclax); and

               -  if best response is < CR with BCL-2-family protein inhibitor treatment

               -  must have had ≥ 1 year of BCL-2-family protein inhibitor treatment; and

               -  must have progressed > 6 months after last BCL-2-family protein inhibitor
                  treatment

               -  if best response is CR with BCL-2-family protein inhibitor treatment

               -  must have relapsed ≥ 1 year after last BCL-2-family protein inhibitor treatment

          -  A PI3K inhibitor (eg, idelalisib, duvelisib, TGR-1202, copanlisib, buparlisib); and
             must have progressed or relapsed > 6 months after last treatment with the PI3K
             inhibitor (NOTE THAT THIS CRITERION IS NOT APPLICABLE TO 2ND-STEP REGISTRATION)

        Prior allogeneic stem cell transplant allowed provided the following criteria are met:

          -  ≥ 12 months have elapsed since allogeneic transplant

          -  No current or prior evidence of graft-versus-host disease

          -  No current requirement for immunosuppressive therapy Prior autologous stem cell
             transplant allowed provided ≥ 6 months have elapsed since autologous transplant.

        Eastern Cooperative Oncology Group performance status of 0, 1, or 2

        Adequate bone marrow function as follows:

          -  Absolute neutrophil count (ANC) ≥ 1,000/mm3 (without support of granulocyte colony
             stimulating factors)

          -  Platelets ≥ 50,000/mm3 (untransfused)

          -  Hemoglobin ≥ 9.0 g/dL

        Adequate coagulation, renal, and hepatic function as follows:

          -  aPTT and PT ≤ 1.2 × upper limit of normal (ULN) for the laboratory

          -  Calculated creatinine clearance ≥ 50 mL/min as calculated by the standard
             Cockcroft-Gault equation using age, actual weight, creatinine, and gender

          -  AST and ALT ≤ 1.5 × ULN for the laboratory

          -  Bilirubin ≤ 1.5 × ULN for the laboratory. For a woman of childbearing potential
             (WCBP), a negative serum pregnancy test performed within 7 days prior to initiation of
             study treatment.

        Note: Postmenopausal is defined as any of the following:

          -  Age ≥ 60 years

          -  Age < 60 years and amenorrheic for at least 1 year with follicle-stimulating hormone
             (FSH) and plasma estradiol levels in the postmenopausal range

          -  Bilateral oophorectomy WCBP and male patients must agree to use a medically accepted
             form of birth control for the duration of study treatment and for at least 1 month
             following completion of venetoclax and/or idelalisib or 12 months following rituximab,
             whichever occurs later.

        Ability to understand and the willingness to sign a written informed consent document.

        Exclusion Criteria:

        A patient who meets any of the following exclusion criteria is ineligible to participate in
        the study:

        Known histologic transformation from CLL/SLL to an aggressive lymphoma (ie, Richter's
        transformation).

        Known history of drug-induced pneumonitis History of inflammatory bowel disease. Central
        nervous system involvement Clinically significant infection including active hepatitis B or
        hepatitis C requiring active treatment, or active CMV infection Known human
        immunodeficiency virus (HIV) seropositivity. * Note: HIV testing is not required.

        Vaccination within 4 weeks prior to initiation of rituximab *Note: Review vaccination
        status. Patients should, if possible, be brought up-to-date with all immunizations in
        agreement with current immunization guidelines at least 4 weeks prior to initiating
        rituximab.•Ongoing requirement for warfarin (due to potential drug-drug interactions that
        may increase the exposure of warfarin and ensuing complications).

        Has received any of the following within 14 days prior to initiation of study
        treatment:(NOTE THAT THIS CRITERION IS NOT APPLICABLE TO 2ND-STEP REGISTRATION)

          -  Anti-cancer therapy

          -  Investigational therapy Has not recovered to ≤ grade 1 toxicity(s) from prior therapy,
             except for chronic residual toxicities that in the opinion of the investigator are not
             clinically relevant given the known safety/toxicity profiles of the study regimen (eg,
             alopecia). (NOTE THAT THIS CRITERION IS NOT APPLICABLE TO 2ND-STEP REGISTRATION) Has
             not recovered to ≤ grade 1 toxicity(s) from idelalisib and rituximab, except for
             chronic residual toxicities that in the opinion of the investigator are not clinically
             relevant given the known safety/toxicity profiles of the study regimen (eg, alopecia).
             (NOTE THAT THIS CRITERION IS NOT APPLICABLE TO 1ST-STEP REGISTRATION)

        Ongoing or planned treatment with any of the following:

          -  Steroid therapy for anti-neoplastic intent

          -  Strong or moderate CYP3A inhibitor or inducer, and/or a narrow-therapeutic sensitive
             substrate

          -  P-gp inhibitor or narrow-therapeutic sensitive P-gp substrate If any of these agents
             have been used, patients must be off them for ≥ 1 week before initiation of study
             treatment.

        Prior intolerance to any component of study regimen that, in the opinion of the
        investigator would preclude study treatment.

        A cardiovascular disability status of New York Heart Association Class ≥ II Diagnosis or
        treatment for another malignancy within 1 year of study registration, with the exception of
        complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, any in
        situ malignancy, or low-risk prostate cancer after curative therapy Active liver disease
        other than lymphoid involvement, inflammatory bowel disease, or Crohn's disease
        Malabsorption syndrome or other condition that precludes enteral route of administration.

        Exhibits evidence of other clinically significant uncontrolled condition(s) including, but
        not limited to:

          -  Uncontrolled infection (viral, bacterial, or fungal)

          -  Grade 3 or greater neutropenic fever within 1 week prior to initiation of study
             treatment Active autoimmune cytopenias (for 2 or more weeks), including autoimmune
             hemolytic anemia (AIHA) and idiopathic thrombocytopenic purpura.

        Pregnancy or breastfeeding Medical, psychological, or social condition that, in the opinion
        of the investigator, may increase the patient's risk, interfere with the patient's
        participation in the study or hinder evaluation of study results