Malignant pleural mesothelioma (MPM) is a cancer for which there is no cure. The most effective combination chemotherapy, Pemetrexed (Alimta)/Cisplatin, has yielded overall response rates of up to 40%, but with improvements in overall median survival of only 3.5 months. Prior Phase I trials of intrapleural infusion (IP) of Ad.hIFN-beta (BG00001) were safe. The most recent trial of IP Ad.IFNalpha (SCH 721015) at a dose of 3e11 viral particles (vp) given three days apart was safe and well tolerated, and showed high levels of IFN in pleural fluid and serum. Our preclinical data modeling this proposed study suggest that two IP doses of Ad.IFN-alpha in combination with chemotherapy are well tolerated and markedly enhances efficacy. The purpose of the new study is to determine the safety of administrating intrapleural SCH 721015 (Ad.hIFN-alpha 2b) in combination with chemotherapy for the management of malignant pleural mesothelioma. This study will enroll subjects with pleural mesothelioma. Subjects will receive two fixed dosed of SCH 721015 followed by 4-6 cycles of chemotherapy. Subjects will require placement of a pleural catheter for administration of SCH 721015.