Recently a new type of guided-wave structure, named chirowaveguide was suggested by the authors. The chirowaveguides consist of cylindrical waveguides filled with homogeneous isotropic chiral materials. Due to the electromagnetic chirality of the material inside the waveguide, several important features area associated with this type of guided-wave structure. In this paper, the theory of chirowaveguides is discussed and their salient features are analyzed. It is show that the Helmhotz equations for the longitudinal components of electric and magnetic fields in chirowaveguides are always coupled and consequently, in these waveguides individual transverse electric (TE), transverse magnetic (TM), or transverse electromagnetic (TEM) modes cannot be supported. As an illustrative example, the parallel-plate chirowaveguide is analyzed in detail and the corresponding dispersion relations, cut-off frequencies, propagating and evanescent modes are obtained. In the dispersion (Brillouin) diagram for a chirowaveguide, three regions are identified: the fast-fast-wave region, the fast-slow-wave region and the slow-slow-wave region. For each of these regions the electromagnetic field components in a parallel-plat chirowaveguide are analyzed and the electric field components are plotted. Potential applications of chirowaveguides in integrated optical devices, communication systems, and printed circuit antennas are mentioned.