Two-dimensional hexachiral lattices belong to the family of honeycomb-like mechanical metamaterials such as triangular, hexagonal, and kagome lattices. The common feature of this family of beam-based metamaterials is their six-fold rotational symmetry which guarantees their (transversely-) isotropic elastic response. In the case of hexachiral lattices, a single geometric parameter may be introduced to control the degree of chirality such that the elastic Poisson's ratio can be adjusted between 0.33 and −0.8. Detailed finite element simulations are performed to establish the structure–property relationships for hexachiral lattices for relative densities ranging from 1% to 45%. It is shown that both the Young's and shear moduli are always lower for hexachiral structures than for optimal lattices (triangular and kagome). This result is in line with the general understanding that stretching-dominated architectures outperform bending-dominated architectures. The same conclusions may be drawn from the comparison of the tensile yield strength. However, hexachiral structures provide a lower degree of plastic anisotropy than stretching-dominated lattices. Furthermore, special hexachiral configurations have been identified that exhibit a slightly higher shear yield strength than triangular and kagome lattices, thereby presenting an example of bending-dominated architectures outperforming stretching-dominated architectures of equal mass. Tensile specimens have been additively manufactured from a tough PLA polymer and tested to partially validate the simulation results.