In this letter we show the viability of using concentric cylindrically-periodic (CP) dielectrics to realize low-loss propagation at submillimeter wavelengths. Most of the power in the CP Waveguide (WG) is confined to an air core propagating a TE_(01) mode. The TM_(11) mode degeneracy is removed over a very wide bandwidth by a series of periodically spaced dielectric rings that are optimized in thickness and spacing. The new waveguide differs from classical Bragg fibers in that we use only a small number of dielectric layers (2-4), and terminate the outer layer with an external metal coating. We include several designs and describe the optimization procedure that was used to realize structures with low propagation and bend loss