CUORE is an experiment designed to search for neutrinoless double beta decay of 130-Te. It is located at the underground Laboratori Nazionali del Gran Sasso of INFN in Italy, and its detector is a ton-scale array of 988 TeO2 crystals operated as cryogenic calorimeters at ~10 mK. The CUORE large mass and ultra-low background allow the study of other rare processes, such as the neutrinoless double beta decay of 128-Te, which is the second tellurium isotope with the highest natural isotopic abundance (31.75%). This study is complicated by the high background level in the energy region where a possible signal peak is expected (~867 keV). In this presentation, we describe the Bayesian analysis we performed to search for 128-Te neutrinoless double beta decay in CUORE, and we present our first results.