The purpose of this study is to build on the efficacy of the GEMOX regimen by adding Sorafenib in the treatment of Biliary Tract Cancer. Since there is no data on the combination of these three agents, the investigators plan to evaluate the safety in a run-in phase I portion in order to define the recommended phase II dose (RPTD). The phase II trial will enroll 40 patients at the RPTD level within 2 years in order to provide a preliminary estimate of progression-free survival (primary endpoint of the trial) in the target population.