A Study of Nivolumab and Chemotherapy Followed by Surgery for Mesothelioma

Inclusion Criteria: * Age ≥ 18 years * Karnofsky performance status \> 70% * Pathologic diagnosis of malignant pleural mesothelioma. * 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