We investigate the mid-infrared chiroptical response of plasmonic nanostructures based on Al-doped ZnO and layers of an aqueous solution of Ladarixin, a chiral pharmaceutical currently under clinical trial for the treatment of type 1 diabetes. We explore the possibilities offered by localised surface plasmon resonances (LSPRs) for the enhancement of vibrational circular dichroism (VCD) of the considered chiral drug solution. Focusing on diverse plasmonic nanoshell geometries, we find that LSPRs provide an amplification factor of VCD differential absorption cross-section ranging from to thanks to near-field intensity enhancement produced by LSPRs. Our results indicate that nanoshell LSPRs are promising for probing molecular chirality at the nanoscale.