Nanostructures constructed from metal and semiconductor nanocrystals conjugated to and organized by DNA are an emerging class of materials with collective optical properties. We created discrete pyramids of DNA with gold nanocrystals at the tips. By taking small-angle X-ray scattering measurements from solutions of these pyramids, we confirmed that this pyramidal geometry creates structures which are more rigid in solution than linear DNA. We then took advantage of the tetrahedral symmetry to demonstrate construction of chiral nanostructures.