Plane wave propagation in a chiral lattice is investigated through the application of Bloch's theorem. Two-dimensional dispersion relations are estimated and analyzed to illustrate peculiar properties of chiral or non-centrosymmetric configurations and investigate the directional behavior of wave propagation for varying geometric parameters. Special attention is devoted to the determination of phase and group wave velocities. Considerations based upon the analysis of velocity plots are compared with results obtained from dispersion curves to further validate the directional behavior of the proposed lattice. Finally, The relation of directionality with frequency of the traveling waves is discussed.