Chirality at the nanometer scale represents one of the most rapidly developing areas of research. Self-assembly of DNA-nanoparticle (NP) hybrids enables geometrically precise assembly of chiral isomers. The concept of a discrete chiral nanostructure of tetrahedral shape and topology fabricated from four different NPs located in the corners of the pyramid is fundamental to the field. While the first observations of optical activity of mixed pyramidal assemblies were made in 2009 (Chen, W.; et al. Nano Lett. 2009, 9, 2153-2159), further studies are difficult without finely resolved optical data for precisely organized NP pyramidal enantiomers. Here we describe the preparation of a family of self-assembled chiral pyramids made from multiple metal and/or semiconductor NPs with a yield as high as 80%. Purposefully made R- and S-enantiomers of chiral pyramids with four different NPs from three different materials displayed strong chiroptical activity, with anisotropy g-factors as high as 1.9 x 10(-2) in the visible spectral range. Importantly, all NP constituents contribute to the chiroptical activity of the R/S pyramids. We were able to observe three different circular dichroism signals in the range of 350-550 nm simultaneously. They correspond to the plasmonic oscillations of gold, silver, and bandgap transitions of quantum dots. Tunability of chiroptical bands related to these transitions is essential from fundamental and practical points of view. The predictability of optical properties of pyramids, the simplicity of their self-assembly in comparison with lithography, and the possibility for polymerase chain reaction-based automation of their synthesis are expected to facilitate their future applications.