The relationship between chirality and superconductivity is an intriguing question. The two enantiomeric crystalline radical cation salts κ‐[(S,S)‐DM‐BEDT‐TTF]2ClO4 and κ‐[(R,R)‐DM‐BEDT‐TTF]2ClO4, showing κ‐type arrangement of the organic layers, are investigated in search for superconducting chiral molecular materials following a 1992 report indicating the occurrence of a superconducting transition in the former compound. While the initial interpretation is presently challenged through in‐depth temperature and pressure dependent single crystal resistivity measurements combined with band structure calculations, the two chiral conductors show metal like behavior with room temperature conductivities of 10–30 S cm−1 at ambient pressure and stabilization of the metallic state down to the lowest temperatures under moderate pressures. Moreover, their structural and theoretical investigations reveal an original feature, namely the existence of two different κ layers with 1D and 2D electronic dimensionality, respectively, as a consequence of an interlayer charge transfer. The resistivity drop observed for one sample below 1 K and insensitive to magnetic field, possibly results from mixing in‐plane and out‐of‐plane contributions to the measured resistance and suggests current induced charge order melting. This feature contradicts the occurrence of superconductivity in these chiral molecular conductors and leaves open the discovery of the first chiral molecular superconductors.