Inclusion Criteria:

          -  Age ≥ 18 years

          -  Karnofsky performance status > 70%

          -  Pathologic diagnosis of malignant pleural mesothelioma.

          -  At least one measurement must be >1.5 cm.

          -  Potentially resectable by pleurectomy/decortication, as assessed by thoracic surgeon

          -  Negative serum pregnancy test in women of childbearing potential

          -  Female patients of childbearing potential must agree to use a highly effective form of
             contraception for the duration of the study and for at least 5 months after the last
             administration of nivolumab and at least 6 months after last administration of
             pemetrexed, whichever is longer

          -  Male patients with female partners of childbearing potential must agree to use a
             highly effective form of contraception for the duration of the study and for at least
             7 months after the last administration of nivolumab and at least 3 months after the
             last administration of pemetrexed, whichever is longer

          -  Adequate archival or fresh tissue for correlative analysis. Archival tissue will be
             deemed acceptable as long as their was no interval therapy prior to cycle 1 day 1 of
             protocol therapy. If sufficient archival or fresh tissue is not available, then a
             repeat biopsy at baseline prior to starting study treatment will be required as long
             as medically safe and feasible

          -  Absolute neutrophil count ≥ 1000/mcL

          -  Total bilirubin ≤ 1.5 mg/dl

          -  AST and ALT ≤ 3.0 x upper limit of normal

          -  Creatinine ≤ 1.5 x upper limit of normal

          -  Negative HIV serology blood test

        Exclusion Criteria:

          -  Prior treatment with chemotherapy or immunotherapy for mesothelioma

          -  Autoimmune disease requiring systemic immune modulating treatment during the past two
             years

          -  Pregnant or lactating women

          -  Known active hepatitis B or hepatitis C

          -  Current use of systemic prednisone at dose ≥ 10 mg daily (or the equivalent dose with
             another corticosteroid)

          -  Serious concurrent medical illness or another active cancer requiring treatment

          -  Active pneumonitis