We employed ab initio global structural prediction algorithms to obtain the ground-state structure of CuBO2 This is a very promising p-type transparent conductive oxide that was synthesized recently, and thought to belong to the delafossite family. We proved that the true ground state is certainly not the delafossite structure, and that the most promising candidate is a low symmetry monoclinic phase. This is still a layered structure, but with boron and copper having a different coordination with respect to the delafossite phase.