Large Co-MOF-74 crystals of a few hundred micrometers were prepared by solvothermal synthesis, and their structure and morphology were characterized by scanning electron microscopy (SEM), IR, and Raman spectroscopy. The hydrothermal stability of the material up to 60 °C at 93% relative humidity was verified by temperature-dependent XRD. Proton conductivity was studied by impedance spectroscopy, using a single crystal. By varying the relative humidity (70–95%), temperature (21–60 °C), and orientation of the crystal relative to the electrical potential, it was found that proton conduction occurs predominantly through the linear, unidirectional (1D) micropore channels of Co-MOF-74, and that water molecules inside the channels are responsible for the proton mobility by a Grotthuss-type mechanism. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.