A Study of Ibrutinib With Rituximab in People With Untreated Marginal Zone Lymphoma

Inclusion Criteria: * Histologically documented marginal zone lymphoma, including splenic, nodal, and extranodal sub-types at the enrolling institution. * No prior systemic therapy for MZL with the exception of the following: * Prior antibiotic therapy for H. pylori, C. psittaci, and B. burgdorferi * Prior antiviral therapy for HCV Note: Subjects are eligible if they had prior splenectomy or other local surgical treatment or local radiation therapy without systemic therapy and now require their first ever systemic therapy. * Men and women ≥18 years of age * Patients with gastric MALT lymphoma must be H. pylori negative or have failed a trial of H. pylori eradication * Patients with gastric MALT lymphoma who are H. pylori negative or who have relapsed/refractory disease after H. pylori eradication must be ineligible for, have refused or failed gastric radiation therapy * Eastern Cooperative Oncology Group (ECOG) performance status of ≤2 * ≥1 measurable lesion on computed tomography (CT) scan (\>1.5 cm in longest dimension) unless bone marrow disease only including those with hemolytic anemia. Lesions in anatomical locations (such as extremities or soft tissue lesions) that are not well visualized by CT may be measured by magnetic resonance imaging (MRI) instead. Patients with splenomegaly without other measurable disease must have splenomegaly of \>15 cm in the craniocaudal direction * Life expectancy of \>3 months, in the opinion of the investigator * Female subjects must be of non-reproductive potential (i.e., post-menopausal by history - no menses for ≥2 years; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy). Female subjects of childbearing potential must have a negative serum pregnancy test upon study entry * Male and female subjects who agree to use highly effective methods of birth control (e.g., condoms, implants, injectables, combined oral contraceptives, some intrauterine devices \[IUDs\], sexual abstinence, or sterilized partner) during the period of therapy and for 12 months (females) and 90 days (males) after the last dose of study drug * Documented evidence of need for treatment, including, but not limited to, threatened end-organ function, bulky disease (\>5 cm), symptoms, requirement for transfusion or growth factor support, or medically significant need for intervention For subjects with presumptive evidence of transformation based on clinical assessment of factors such as, but not limited to, increasing lactate dehydrogenase (LDH), rapidly worsening disease, or frequent B-symptoms, both a pre-treatment tumor biopsy and bone marrow biopsy are required to rule out large cell transformation. For all subjects, results of both the tumor biopsy and bone marrow biopsy must be known prior to enrollment and randomization. Exclusion Criteria: * Medically apparent central nervous system lymphoma or leptomeningeal disease * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible * History of other malignancies except adequately treated non-melanoma skin cancer, curatively treated in-situ cancer, or other solid tumors curatively treated with no evidence of disease for ≥2 years * Subject who received a strong cytochrome P450 (CYP) 3A inhibitor within 7 days prior to first dose of ibrutinib/placebo or subject who requires continuous treatment with a strong CYP3A inhibitor * Concurrent systemic immunosuppressant therapy (e.g., cyclosporine A, tacrolimus, etc., or chronic administration of \>20 mg/day of prednisone) within 28 days of the first dose of study drug * Currently active, clinically significant cardiovascular disease such as uncontrolled arrhythmias or Class 3 or 4 congestive heart failure as defined by New York Heart Association Functional Classification; or a history of unstable angina, acute coronary syndrome, or myocardial infarction within 6 months of prior to screening * Recent infection requiring systemic anti-infective treatment that was completed ≤14 days before the first dose of study drug * Any uncontrolled active systemic infection * Known bleeding diathesis (e.g., von Willebrand's disease) or hemophilia * Hepatitis B (HBV): All subjects must be screened for hepatitis B and C. Subjects with a positive polymerase chain reaction for hepatitis B must be on entecavir or equivalent therapy as per institutional standard of care. (Hep C patients may be enrolled if other parameters precluding hepatic impairment are met. And they are not undergoing active therapy for hepatitis C * Human immunodeficiency virus (HIV): NOTE: HIV is a contraindication if the subject has an active opportunistic infection (OI) within 12 months and CD4 count is below the normal range * Any of the following abnormalities: * Absolute neutrophil count (ANC) \<750 cells/mm3 (0.75 x 10\^9/L) unless there is documented bone marrow involvement * Platelet count \<50,000 cells/mm\^3 (50 x 10\^9/L) independent of transfusion support unless there is documented bone marrow involvement * Serum aspartate transaminase (AST) or alanine transaminase (ALT) ≥3.0 x upper limit of normal (ULN) * Creatinine \>2.0 x ULN or Estimated Glomerular Filtration Rate GFR \[Cockcroft-Gault\]) \<30 mL/min * Hemoglobin \<8.0 g/dL unless secondary to hemolysis or documented bone marrow involvement * Bilirubin \>1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) * PT/INR \>1.5 x ULN and PTT (aPTT) \>1.5 x ULN unless factor XI deficiency or lupus anticoagulant. * Unable to swallow capsules or disease significantly affecting gastrointestinal function such as malabsorption syndrome, resection of the stomach or small bowel, or complete bowel obstruction * Major surgery within 4 weeks prior to the first dose of study drug * Any life-threatening illness, medical condition, including uncontrolled diabetes mellitus (DM), or organ system dysfunction that, in the opinion of the investigator, could compromise the subject's safety or put the study outcomes at undue risk * Lactating or pregnant * Unwilling or unable to participate in all required study evaluations and procedures * Unable to understand the purpose and risks of the study and to provide a signed and dated informed consent form (ICF) and authorization to use protected health information (in accordance with national and local subject privacy regulations) * Subjects with chronic liver disease with hepatic impairment Child-Pugh class B or C