An exceptional oxygen barrier polyester prepared from a new biomass-derived monomer, 3,3'-bifuran-5,5'-dicarboxylic acid, is reported. When exposed to air, the furan-based polyester cross-links and gains O2 permeability 2 orders of magnitude lower than initially, resulting in performance comparable to the best polymers in this class, such as ethylene-vinyl alcohol copolymers. The cross-links hinder the crystallization of amorphous samples, also rendering them insoluble. The process was observable via UV-vis measurements, which showed a gradual increase of absorbance between wavelengths of 320 and 520 nm in free-standing films. The structural trigger bringing about these changes appears subtle: the polyester containing 5,5'-disubstituted 3,3'-bifuran moieties cross-linked, whereas the polyester with 5,5'-disubstituted 2,2'-bifuran moieties was inert. The 3,3'-bifuran-based polyester is effectively a semicrystalline thermoplastic, which is slowly converted into a cross-linked material with intriguing material properties once sufficiently exposed to ambient air.