Hf2B2-2δIr5+δ crystallizes with a new type of structure: space group Pbam, a = 5.6300(3) Å, b = 11.2599(5) Å, and c = 3.8328(2) Å. Nearly 5% of the boron pairs are randomly replaced by single iridium atoms (Ir5+δB2-2δ). From an analysis of the chemical bonding, the crystal structure can be understood as a three-dimensional framework stabilized by covalent two-atom B-B and Ir-Ir as well as three-atom Ir-Ir-B and Ir-Ir-Ir interactions. The hafnium atoms center 14-atom cavities and transfer a significant amount of charge to the polyanionic boron-iridium framework. This refractory boride displays moderate hardness and is a Pauli paramagnet with metallic electrical resistivity, Seebeck coefficient, and thermal conductivity. The metallic character of this system is also confirmed by electronic structure calculations revealing 5.8 states eV-1 fu-1 at the Fermi level. Zr2B2-2δIr5+δ is found to be isotypic with Hf2B2-2δIr5+δ, and both form a continuous solid solution.