The quaternary rare-earth-metal hafnium copper arsenides REHfCu2+delta As3 (where RE = La-Nd; delta approximate to 0.17) were obtained by direct reactions of the elements at 1073 K. They adopt a noncentrosymmetric orthorhombic crystal structure (space group Pmn2(1); a = 397.73(3)-392.37(2) pm, b = 1062.68(8)-1055.23(6) pm, c = 1307.25(9)-1291.40(7) pm for RE = La-Nd), which can be considered to be a Cu-deficient superstructure of the ternary Zr2Ni3P3-type structure found among metal-rich pnictides with a metal-to-nonmetal ratio close or equal to 2:1. The RE atoms occupy trigonal prismatic (CN6) and monocapped trigonal prismatic (CN7) sites, the latter resulting from the occurrence of Cu vacancies, the Hf atoms occupy octahedral sites (CN6), and the Cu atoms occupy tetrahedral sites (CN4). Band structure calculations on idealized models LaHfCu2As3 and LaHfCu2.5As3 suggest that the bonding situation improves by fractional occupation of the Cu3 site via depopulation of antibonding Cu-As states.