ACY-1215 in Combination With BCR Pathway Inhibitors in Relapsed CLL

Inclusion Criteria: * Participants must have confirmed CLL/SLL relapsed after at least one prior therapy and currently in need of treatment by IWCLL 2008 criteria * Age ≥ 18 * ECOG performance status ≤2 (Karnofsky ≥60%, see Appendix A) * For the ibrutinib arm only: participants must not currently require ongoing anticoagulation for any reason, or have had any major bleeding events within 6 months of enrollment * Participants must have normal organ and marrow function as defined below: * Absolute neutrophil count (ANC) \> 1000 K/μL and platelet count \> 30,000 K/μL independent of transfusion support. * total bilirubin \< 2X institutional upper limit of normal (ULN) unless predominantly indirect and therefore likely due to hemolysis or Gilbert's syndrome * AST(SGOT)/ALT(SGPT) ≤3X institutional upper limit of normal for ibrutinib arm; within normal limits on the idelalisib arm * creatinine \< 2X ULN * Participants must have measurable disease, including at least one of the following: an absolute B cell count \> 5000/uL, OR lymphadenopathy with at least one lymph node \> 2 cm in long axis, OR palpable splenomegaly, OR cytopenias (Hb \< 11 g/dL or platelets \< 100K) together with bone marrow infiltration * The effects of the drugs studied in this research protocol on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of treatment administration. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Participants who have had chemotherapy or radiotherapy within 2 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier. * Participants who are receiving any other investigational agents. * Prior therapy with an HDAC inhibitor. * Participants with a history of poor tolerance to either ibrutinib or idelalisib should not be enrolled on the arm containing that drug, but may be enrolled to the other arm. Must agree not to share study medication with another person. * Participants requiring any medications or substances that are strong inducers or inhibitors of CYP3A4 are ineligible. Those who may discontinue these medications are eligible after a 7 day washout period. . Mild or moderate inducers or inhibitors of CYP3A4 are permitted but moderate inhibitors will require dose reduction of ibrutinib (see section 5.5). * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because ACY-1215, as well as both ibrutinib and idelalisib, have unknown effects on a developing fetus or newborn. Breastfeeding should be discontinued if the mother is treated on this research protocol. * HIV-positive participants on CYP3A4 modulating antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with ACY-1215, ibrutinib or idelalisib. In addition, these participants are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * Participants who require active chemotherapy for another cancer. Those requiring hormonal therapy or radiation therapy may be considered for enrollment on a case by case basis. * Corrected QT interval using Fridericia's formula (QTcF) value \> 480 msec at screening; family or personal history of long QTc syndrome or ventricular arrhythmias including ventricular bigeminy at screening; previous history of drug-induced QTc prolongation or the need for treatment with medications known or suspected of producing prolonged QTc intervals on ECG. * Positive hepatitis B virus (HBV) surface antigen, or core antibody; and known or suspected active hepatitis C virus (HCV) infection, for the idelalisib arm. On the ibrutinib arm, patients with positive hepatitis B surface antigen may be appropriately treated and enrolled on this study as long as their HBV DNA / viral load is undetectable. Patients positive for hepB core antibody and negative for surface antigen are eligible for the ibrutinib arm, as are patients with hepatitis C. * Subjects requiring anticoagulation with warfarin or vitamin K antagonists are excluded from the ibrutinib arm. If previously on these drugs and switched, INR must be normal for 7 days prior to enrollment. * Subjects enrolling on the ibrutinib arm must not have had major surgery within 14 days, or minor surgery within 7 days. * Participant must be able to swallow pills.