We describe from the theoretical point of view a plasmonic mechanism of optical activity in chiral complexes composed of metal nanoparticles (NPs). In our model, the circular dichroism (CD) signal comes from the Coulomb interaction between NPs. We show that the CD spectrum is very sensitive to the geometry and composition of a chiral complex and also has typically both positive and negative bands. In our calculations, the strongest CD signals were found for the helix geometry resembling helical structures of many biomolecules. For chiral tetramers and pyramids, the symmetry of a frame of a complex is very important for the formation of a strong CD response. Chiral natural molecules (peptides, DNA, etc.) often have strong CD signals in the UV range and typically show weak CD responses in the visible range of photon energies. In contrast to the natural molecules, the described mechanism of plasmonic CD is able to create strong CD signals in the visible wavelength range. This plasmonic mechanism offers a unique possibility to design colloidal and other nanostructures with strong optical chirality.