Inclusion Criteria:

          -  Age greater than or equal to 18 years

          -  Histologically confirmed Marginal Zone Lymphoma

          -  Patients must have measurable disease as defined by at least one lymph node ≥1.5 cm or
             spleen >13 cm.

             °Patients with intestinal MALT lymphoma must have disease that is detectable by EGD or
             colonoscopy with biopsy

          -  Patients with gastric MALT lymphoma must be h. pylori negative

             °Patients who are h. pylori positive are allowed if they 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

          -  ECOG performance status ≤ 1

          -  Life expectancy of greater than 2 years

          -  Patients must have normal organ function as defined below:

               -  Platelet count ≥ 50,000 cells/mm^3

               -  Hemoglobin ≥ 8.0 g/dL

               -  Absolute neutrophil count ≥ 1000 cells/mcL. If there is documented bone marrow
                  involvement, ANC must be >/= 500 cells/mcL

               -  Total bilirubin < 1.5 x upper normal institutional limits. In patients with
                  Gilbert's disease or documented liver involvement, total bilirubin up to 3x ULN
                  will be allowed

               -  AST(SGOT)/ALT(SGPT) <3 x institutional upper limit of normal unless elevation is
                  caused by liver involvement with MZL

          -  AST(SGOT)/ALT(SGPT) <3 x institutional upper limit of normal unless elevation is
             caused by liver involvement with MZL

             °OR Creatinine clearance >60 mL/min for patients with creatinine levels above
             institutional normal (by Cockcroft-Gault estimate or 12-24h creatinine clearance
             measurements).

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

          -  Patient must be able to swallow pills

          -  HIV-positive patients on combination antiretroviral therapy are eligible if their HIV
             is under adequate control with an antiretroviral regimen that has been stable for > 4
             weeks, as long as the CD4 count is > 300. Appropriate studies will be undertaken in
             patients receiving combination antiretroviral therapy when indicated.

          -  Patients with Hepatitis B surface antibody serum positivity due to prior immunization,
             as well as those with Hepatitis B core antibody positivity with negative PCR on
             antiviral therapy will be eligible.

        Exclusion Criteria:

          -  Patients who have had prior systemic therapy, including rituximab

          -  Patients who have had prior radiation therapy, with the following exception:

             °Palliative radiotherapy RT is allowed but must be completed at least 1 week prior to
             treatment on this study, and prior baseline imaging studies or biopsies. Patients must
             meet criteria for measurable/assessable disease as outlined above after completion of
             RT

          -  Prior treatment with ibrutinib or other BTK inhibitor

          -  Patients with h. pylori-associated gastric MALT or stage I/II MZL will be excluded
             unless they are deemed to be unfit for radiation therapy with curative intent.

          -  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

             °Patients with Hep B core ab positivity are allowed provided Hep B PCR is undetectable

          -  Pregnant women or participants unwilling to adhere to institutional guidelines for
             highly effective contraception for 12 months after the last dose of rituximab are
             excluded from this study because of documented risks of rituximab on fetal immunologic
             development and unknown effects of venetoclax on embryonic development. Because there
             is an unknown but potential risk for adverse events in nursing infants secondary to
             treatment of the mother with venetoclax, breastfeeding should be discontinued.

          -  Received moderate or strong CYP3A inhibitors (such as fluconazole, ketoconazole, and
             clarithromycin) within 7 days prior to the first dose of venetoclax.

          -  Received moderate or strong CYP3A inducers (such as rifampin, carbamazepine,
             phenytoin, St. John's Wort) within 7 days prior to the first dose of venetoclax.