• Safety of Nivolumab in Older Subjects [ Time Frame: Until up to 6 subjects can be adequately assessed for DLT. ]
  The primary endpoint for the Stage 1 phase of the study is dose-limiting toxicity which will be assessed for each Stage 1 subject using the DLT criteria
• Efficacy of Nivolumab [ Time Frame: 2 years ]
  The primary endpoint for the Stage 1 phase of the study is the 2-year progression-free endpoint which will be determined for each subject as a binary variable indicating if they are alive and progression-free at 2 years (PFS2)

• Stage 1 is to evaluate the safety of Nivolumab consolidation after R-MPV [ Time Frame: Until up to 6 subjects can be adequately assessed for DLT. ]
  Stage 1 is to evaluate the safety of Nivolumab consolidation after R-MPV induction chemotherapy in older subjects with previously untreated PCNSL in terms of a tolerated dose (based on dose-limiting toxicities (DLT)) for the expansion phase of the study (Stage 2).
• The primary objective of Stage 2 is to evaluate the efficacy of Nivolumab consolidation after R-MPV [ Time Frame: 2 years. ]
  The primary objective of Stage 2 is to evaluate the efficacy of Nivolumab consolidation after R-MPV induction chemotherapy in terms of the 2-year progression-free survival rate.

• Progression Free Survival (PFS) [ Time Frame: 2 years ]
  PFS is defined as the duration of time from enrollment to first occurrence of either progressive disease or death.
• Overall Survival (OS) [ Time Frame: 2 years ]
  OS is defined as the duration from enrollment to the date of death from any cause.
• Objective and Complete Response Rates [ Time Frame: approx. 2 years ]
  Objective response will be determined for each subject as a binary variable indicating if they have achieved a best overall response of CR or PR as determined by the International Criteria for PCNSL (IPCG). Complete response will be determined for each subject as a binary variable indicating if they have achieved a best overall response of CR as determined by the International Criteria for PCNSL(IPCG).
• Conversion Rate from Partial to Complete Response [ Time Frame: approx. 2 years ]
  Response conversion will be determined for each subject who achieve a best overall response of PR during induction therapy as a binary variable indicating if the subsequently achieve a best overall response of CR to nivolumab consolidation therapy.

• To evaluate progression-free survival (PFS) in older subjects with previously untreated PCNSL who received R-MPV induction chemotherapy followed by Nivolumab consolidation therapy. [ Time Frame: 2 years. ]
• To evaluate overall survival (OS) and estimate the OS rate at 2 years in older subjects with previously untreated PCNSL who received R-MPV induction chemotherapy followed by Nivolumab consolidation therapy. [ Time Frame: 2 years. ]
• To estimate objective and complete response rates in this subject population. [ Time Frame: Through study completion, an average of 2 years. ]
• To estimate conversion rate from partial to complete response before and after Nivolumab consolidation therapy. [ Time Frame: Through study completion, an average of 2 years. ]

• Brain and Nervous System
• Eye and Orbit

• Experimental: Stage 1
  Safety Run-In
  Intervention: Drug: Nivolumab
• Experimental: Stage 2
  Expansion Cohort
  Intervention: Drug: Nivolumab

Inclusion Criteria:

Subjects must meet all of the following criteria to participate in this study:

1. Written informed consent and HIPAA authorization for release of personal health information of subject or subject's legally authorized representative.
2. Age ≥ 65 years at the time of consent
3. Eastern Cooperative Oncology Group (ECOG) performance status of 0 - 3 within 14 days prior to day 1 of treatment
4. Histological or cytological confirmation of PCNSL, CD20 positive by immunohistochemistry
5. Received at least 2 cycles of high-dose methotrexate (HD-MTX) containing induction chemotherapy per institutional standard (R-MPV preferred; see Appendix VI ) without evidence of progressive disease. No less than 4 weeks and no more than 8 weeks may have elapsed between last dose of HD-MTX containing induction chemotherapy and day 1 of study treatment
6. Recovered from all reversible acute toxic effects of prior therapy (other than alopecia) to ≤ Grade 1 or baseline)
7. Measurable disease at the time of diagnosis (i.e. prior to pre-study HD-MTX containing induction chemotherapy) including lesions that can be accurately measured in 2 dimensions by CT or MRI of brain and with a greatest transverse diameter of ≥ 1 cm. The following disease assessments must have been obtained prior to initiation of pre-study HD-MTX containing induction chemotherapy: MRI of the brain (and spine if indicated)
8. Deemed poor candidate for whole brain irradiation (WBI) or autologous stem cell transplant (ASCT) due to advanced age, ECOG performance status of 2, or in the opinion of the treating physician, subject would not tolerate the administration of WBI or ASCT for other reasons
9. Life expectancy of at least 3 months

10. Demonstrate adequate organ function as defined below (all screening labs to be obtained within 14 days prior to day 1 of treatment):

    1. Absolute Neutrophil Count (ANC) ≥ 1000K/mm3
    2. Platelet Count ≥ 75 K/mm3
    3. Hemoglobin (Hgb) ≥ 8 g/dL
    4. Serum creatinine ≤ 1.5 mg/dL OR creatinine clearance ≥ 50 cc/minute as measured by a 24-hour urine collection or estimated by the Cockcroft and Gault formula
    5. Bilirubin ≤ 1.5 x upper limit of normal (ULN) (except subjects with Gilbert Syndrome who must have a total bilirubin level of < 3.0 x ULN)
    6. Aspartate aminotransferase (AST) ≤ 3 x ULN
    7. Alanine aminotransferase (ALT) ≤ 3 x ULN
11. Females of childbearing potential (FCBP) must have a negative serum pregnancy test within 3 days prior to day 1 of treatment. NOTE: Females are considered of child bearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are postmenopausal (at least 12 consecutive months with no menses without an alternative medical cause).
12. FCBP must be willing to use a highly effective contraceptive method (i.e., achieves a failure rate of <1% per year when used consistently and correctly) from the time of informed consent until 5 months after treatment discontinuation. Contraceptive methods with low user dependency are preferable but not required. (http://www.hma.eu/fileadmin/dateien/Human_Medicines/01-About_HMA/Working_Groups/CTFG/2014_09_HMA_CTFG_Contraception.pdf)
13. Male subjects must be willing to use condoms from the time of treatment initiation until 7 months after last dose of nivolumab. For a non-pregnant FCBP partner, contraception recommendations should also be considered.
14. As determined by the enrolling physician, ability of the subject to understand and comply with study procedures for the entire length of the study.

Exclusion Criteria:

Subjects must not meet any of the following criteria:

1. Documented or suspected ophthalmologic involvement at the time of enrollment as determined by the investigator. Subjects with ophthalmologic involvement prior to or during pre-study induction are allowed if there is no evidence of ophthalmologic involvement prior to enrollment as determined by the investigator.
2. Any concurrent systemic involvement by lymphoma outside CNS or intraocular lymphoma without evidence of brain disease
3. Any previous chemotherapy or radiation therapy for PCNSL except for treatment with a HD-MTX containing induction chemotherapy. Subjects treated with corticosteroids for PCNSL are allowed.
4. Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study)
5. Has a known additional malignancy within the past 5 years that is active and/or progressive requiring treatment; exceptions include basal cell or squamous cell skin cancer, in situ cervical or bladder cancer, or carcinoma of the prostrate with a current PSA value of <0.5 ng/mL or other cancer for which subject has completed treatment, been disease-free for at least five years, and is considered by Sponsor-Investigator to be at <30% risk of relapse, or on hormonal therapy for a history of either prostate cancer or breast cancer, provided that there has been no evidence of disease progression during the previous three years.
6. Treatment with any investigational drug (including drugs not FDA-approved for the indication for which they are given) within 28 days prior to day 1 of treatment
7. Subjects with active, uncontrolled infections (subjects must be afebrile for >48 hours off systemic antibiotics).
8. Uncontrolled intercurrent illness including, but not limited to, ongoing or active symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements as determined by the investigator.
9. Major surgery and/or radiotherapy within 14 days prior to initiation of study treatment
10. Known history of positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). NOTE: Testing for HIV must be performed at sites where mandated locally.
11. Active infectious hepatitis, type B or C. Subjects with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) may be included if HBV DNA is undetectable.
12. Subjects with active interstitial pneumonitis.
13. Subjects with active, known or suspected autoimmune disease. Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll.