The covalent nature of the low‐barrier N−H−N hydrogen bonds in the negative thermal expansion material H₃[Co(CN)₆] has been established by using a combination of X‐ray and neutron diffraction electron density analysis and theoretical calculations. This finding explains why negative thermal expansion can occur in a material not commonly considered to be built from rigid linkers. The pertinent hydrogen atom is located symmetrically between two nitrogen atoms in a double‐well potential with hydrogen above the barrier for proton transfer, thus forming a low‐barrier hydrogen bond. Hydrogen is covalently bonded to the two nitrogen atoms, which is the first experimentally confirmed covalent hydrogen bond in a network structure. Source function calculations established that the present N−H−N hydrogen bond follows the trends observed for negatively charge‐assisted hydrogen bonds and low‐barrier hydrogen bonds previously established for O−H−O hydrogen bonds. The bonding between the cobalt and cyanide ligands was found to be a typical donor–acceptor bond involving a high‐field ligand and a transition metal in a low‐spin configuration.