Inclusion Criteria:

   - Subjects deemed potentially eligible by their treating physicians will be screened for
   enrollment after d+60 from transplantation

   - Patients who have undergone either ablative or non-myeloablative allogeneic stem cell
   transplantation are eligible.

   - Peripheral blood stem cells must have been used as the stem cell source.

   - Patients must have received transplantation from donors (both related and unrelated)
   who are identical at 8 HLA loci (A, B, C and DR1), or mismatched at no more than 1
   locus (7/8). Among related donors, HLA C typing is not required (6/6 HLA matches).
   Class I typing is to be performed by PCR-SSP techniques and CDC techniques. Class II
   typing is performed by PCR-RFLP +/- PCR-SSP techniques.

   - No evidence of relapsed or residual malignancy within 30 days of trial entry. All
   patients must undergo appropriate staging for their malignancy (i.e. bone marrow
   aspiration for the Leukemias and PET-CT scanning for the lymphomas). Evidence of a
   persistent Cytogenetic abnormality will constitute evidence of residual or relapsed
   disease in the Leukemias, where present. Individuals with CLL are eligible if there is
   no more than 20% residual leukemia in the bone marrow at the time of study entry.

   - Patients who have undergone a non-myeloablative stem cell transplant must have > 80%
   donor hematopoiesis within 30 days of study enrollment. Chimerism within 30 days of
   study entry must be greater than, equal to, or no more than 5% less than the chimerism
   measured at approximately day+30 (if performed).

   - Age ≥ 18.0

   - ECOG performance status ≤2 (Karnofsky ≥60%) (See Appendix A)

   - Participants must have normal marrow function as defined by:

      - WBC ≥ 2,500/μL

      - Absolute Neutrophil Count ≥ 1,000/μL

      - Platelets ≥ 50,000/μL

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

   - The effects of Obinutuzumab 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 Obinutuzumab
   administration.

Exclusion Criteria:

   - Allogeneic stem cell transplantation using a single or multiple umbilical cord blood
   units or using bone marrow.

   - Allogeneic stem cell transplantation using in vivo or ex vivo T cell depletion, either
   by cell manipulation or with T cell depleting antibodies (Any anti-thymocyte globulin
   preparation or alemtuzumab given within 30 days of transplantation)

   - Participation in a clinical trial evaluating another preventative strategy for chronic
   GVHD, or ongoing participation in a clinical trial for therapy of acute GVHD. Prior
   completion of experimental therapy for acute GVHD is permissible if the experimental
   agent was used > 30 days prior to enrollment.

   - Any evidence of ongoing gastrointestinal or hepatic acute GVHD, or evidence of greater
   than ongoing Stage I cutaneous acute GVHD. Ongoing, tapering therapy for resolved
   acute GVHD is permissible.

   - Any evidence of prior active or resolved chronic GVHD.

   - History of severe allergic reaction to Obinutuzumab

   - No Donor Lymphocyte Infusion (DLI) prior to day 100, and no plans for a DLI in the
   upcoming 30 days.

   - Evidence of any active uncontrolled infection (bacterial, viral or fungal) or evidence
   of natural exposure to Hepatitis B, Hepatitis C or HIV. Evidence of Hepatitis B
   exposure includes the presence of Hepatitis B surface antigenemia, a positive
   serological test for Hepatitis B core antibody or nucleic acid testing (NAT testing)
   that is positive for Hepatitis B. Vaccination to Hepatitis B is not an exclusion
   criteria.

   - Pregnancy or lactation. Negative pregnancy test is required within the screening
   window

   - Active use of any other investigational agents.