This is a Phase I, single center, open-label, non-randomized, feasibility, safety and dose-finding study. The purpose of the clinical trial is to determine the safety of the administration of the anti-PSCA CAR T cells (BPX-601) in subjects with non-resectable pancreatic adenocarcinoma, followed by the evaluation of the safety of the rimiducid infusion after BPX-601 administration, and the persistence of the CAR-T cells over time after a single rimiducid infusion.