We theoretically calculate the electromagnetic response of metallic rod dimers for the arbitrary planar arrangement of rods in the dimer. It is shown that dimers without an in-plane symmetry axis exhibit elliptical dichroism and act as "atoms" in planar chiral metamaterials. Because of a very simple geometry of the rod dimer, such planar metamaterials are much easier to fabricate than conventional split-ring or gammadion-type structures and lend themselves to a simple analytical treatment based on a coupled dipole model. Dependencies of the metamaterial's directional asymmetry on the dimer's geometry are established analytically and confirmed in numerical simulations.