In this protocol, patients with non-resectable pancreatic cancer will have autologous T cells collected via apheresis and genetically modified using a retrovirus to express the anti-PSCA Chimeric Antigen Receptor (CAR). The T cells will be reinfused according to a dose-finding schedule after the subject has been identified as having adequate lymphopenia to provide for homeostatic expansion of the adoptively transferred, engineered T cell therapeutic product.