A unique gyroid cubic phase has been discovered for a discotic star mesogen with three covalently attached DNA bases. In this cubic Ia3d phase, the conjugated core of the mesogens and the thymine pseudo guests self‐assemble in mirror image continuous networks, representing a semiconducting material with three‐dimensional transport pathways. The hole carrier mobilities are found to be in the typical range of poly(phenylenevinylene) scaffolds. This structure is stabilized by a weak hydrogen bonding between the thymine bases and can be switched to a columnar liquid crystal – thermally and by the addition of complementary adenine guests.