In this paper, using the finite-difference method, we analyze the propagation of guided modes in a rectangular chirowaveguide which consists of a conventional rectangular waveguide with perfectly conducting walls and filled with homogeneous isotropic chiral materials characterized by the constitutive relations D =cĒ+icB, and H = B/c+icĒ, wherec,c, andcare the permittivity, permeability, and chirality of the medium, respectively. The dispersion or Brillouin diagram of this waveguiding structure is obtained numerically. Notable features of such rectangular chirowaveguides are addressed and compared with those of the nonchiral counterparts.