Nanoscale plasmonic assemblies display exceptionally strong chiral optical activity. So far, their structural design was primarily driven by challenges related to metamaterials whose practical applications are remote. Here we demonstrate that gold nanorods assembled by the polymerase chain reaction into DNA-bridged chiral systems have promising analytical applications. The chiroplasmonic activity of side-by-side assembled patterns is attributed to a 7-9 degree twist between the nanorod axes. This results in a strong polarization rotation that matches theoretical expectations. The amplitude of the bisignate 'wave' in the circular dichroism spectra of side-by-side assemblies demonstrates excellent linearity with the amount of target DNA. The limit of detection for DNA using side-by-side assemblies is as low as 3.7 aM. This chiroplasmonic method may be particularly useful for biological analytes larger than 2-5 nm which are difficult to detect by methods based on plasmon coupling and 'hot spots'. Circular polarization increases for inter-nanorod gaps between 2 and 20 nm when plasmonic coupling rapidly decreases. Reaching the attomolar limit of detection for simple and reliable bioanalysis of oligonucleotides may have a crucial role in DNA biomarker detection for early diagnostics of different diseases, forensics and environmental monitoring.