We report the design, fabrication, and demonstration of antiresonant reflecting optical (ARROW) waveguides with hollow cores. We describe the design principles to achieve low waveguide loss in both transverse and lateral directions. A novel fabrication process using silicon dioxide and silicon nitride layers as well as sacrificial polyimide core layers was developed. Optical characterization of 3.5µm thick waveguides with air cores was carried out. We demonstrate single-mode propagation through these hollow ARROW waveguides with propagation loss as low as 6.5cm^-1 and mode cross sections down to 6.7µm². Applications of these waveguides to sensing and quantum communication are discussed.