Herein, we report on the synthesis and electronic properties of the phosphonate metal-organic framework (MOF) Cu3(H5-MTPPA)2 (H8-MTPPA = methane tetra-p-phenylphosphonic acid). This MOF, termed TUB1, has a unique one-dimensional inorganic building unit composed of square planar and distorted trigonal bipyramidal copper atoms, and a calculated BET surface area of 766.2 m2/g. The formation of TUB1 reduces the band gap of the linker from 4.2 eV to 2.4 eV. DFT calculations reveal two spin-dependent gaps of 2.60 eV and 0.48 eV for the alpha and beta spins, respectively, and that the lowest unoccupied crystal orbital for both gaps predominantly resides on the square planar copper atoms. Single-crystal conductivity measurements on TUB1 crystals yield an average electrical conductance of 53.2 ± 29.5 S/m. Although the H8-MTPPA linker blocks the extended conjugation in TUB1, we show that the presence of the square planar copper atoms in the inorganic building unit promotes the electrical conductivity.