The effect of chirality on the liquid crystal organization has been systematically investigated between (S,S)- and (R,R)-isomers of a dichiral azobenzene compound. The racemic mixture was found to show the cubic phase (Im3m), indicating that the studied compound shows the cubic structure without the effect of chirality. However, with increasing optical purity of the racemic mixture, the cubic (Im3m) structure changes into the tetragonal phases (I422 and I4(1)22), which have been known as the SmQ phases, via a chiral cubic phase (I432). This is the first example of "chirality-driven" cubic-tetragonal structural change observed in liquid crystal systems, which is experimental evidence showing the novel type of chiral effect that produces the anisotropy in the structures of soft materials. The emergence of the anisotropy, i.e., the cubic-tetragonal phase transformation, is also induced by means of photoinduced phase transition of the SmQ phases based on cis-trans photoisomerization of the azobenzene compounds.