We establish helical gold nanorods as the first examples of chiral recognition nanostructures by examining the simple chiral molecule CClHDT adsorbed on the helical Au-40 nanorod. We calculate the vibrational circular dichroism (VCD) spectra of the R and S enantiomers of CClHDT adsorbed on the R (or S) enantiomer of Au-40 using relativistic density functional theory. The highest adsorption energy is found when the Cl atom of CClHDT binds to a low-coordinated Au atom at the edge of Au-40. There are three adsorption modes (essentially identical in energy) corresponding to three orientations of the HDT moiety. We show that, for each adsorption mode, the VCD spectra are distinctly different for the Au-40(R)-ClHDT(R) and Au-40(R)-CClHDT(S) complexes, and we give a qualitative explanation for this based on the principle of chirality transfer. For comparison with the results for Au-40, we calculate the VCD spectra of the R and S enantiomers of CClHDT adsorbed on the achiral Au20 tetrahedral cluster. Again, there are three adsorption modes (essentially identical in energy) corresponding to three orientations of the HDT moiety. However, we show that, for each adsorption mode, the VCD spectra are mirror symmetric but otherwise essentially identical for the Au-20-CClHDT(R) and Au-20-CClHDT(S) complexes. Thus, the inherent chirality of the helical Au-40 nanorod is essential for its chiral recognition functionality.