We present the first copper iridium binary metal oxide with the chemical formula Cu2IrO3. The material is synthesized from the parent compound Na2IrO3 by a topotactic reaction where sodium is exchanged with copper under mild conditions. Cu2IrO3 has the same monoclinic space group (C2/c) as Na2IrO3 with a layered honeycomb structure. The parent compound Na2IrO3 is proposed to be relevant to the Kitaev spin liquid on the basis of having Ir4+ with an effective spin of 1/2 on a honeycomb lattice. Remarkably, whereas Na2IrO3 shows a long-range magnetic order at 15 K and fails to become a true spin liquid, Cu2IrO3 remains disordered until 2.7 K, at which point a short-range order develops. Rietveld analysis shows less distortions in the honeycomb structure of Cu2IrO3 with bond angles closer to 120 degrees compared to Na2IrO3. Thus, the weak short-range magnetism combined with the nearly ideal honeycomb structure places Cu2IrO3 closer to a Kitaev spin liquid than its predecessors.