We have fabricated microstructured polymer optical fibers that guide light in a hollow core using the photonic bandgap mechanism. The hollow core allows the use of polymer fibers to be extended to wavelength ranges where material absorption typically prohibits their use, with attenuation lower than the material loss observed in the infrared. The fabrication method is similar to other microstructured polymer optical fibers, which has favorable implications for the feasibility of manufacturing such bandgap fibers.