The ternary iron arsenide BaFe2As2 becomes superconducting by hole doping, which was achieved by partial substitution of the barium site with potassium. We have discovered bulk superconductivity at T{c}=38 K in (Ba1-xKx)Fe2As2 with x approximately 0.4. The parent compound BaFe2As2 crystallizes in the tetragonal ThCr2Si2-type structure, which consists of (FeAs);{delta-} iron arsenide layers separated by Ba2+ ions. BaFe2As2 is a poor metal and exhibits a spin density wave anomaly at 140 K. By substituting Ba2+ for K+ ions we have introduced holes in the (FeAs);{-} layers, which suppress the anomaly and induce superconductivity. The T{c} of 38 K in (Ba0.6K0.4)Fe2As2 is the highest in hole doped iron arsenide superconductors so far. Therefore, we were able to expand this class of superconductors by oxygen-free compounds with the ThCr2Si2-type structure.