Analysis using the theory of atoms in molecules and natural bond orbital theory of the fully optimized structure of the inside-protonated form of 1,6-diazabicyclo[4.4.4]tetradecane reveals that the encapsulated proton is engaged in a short-strong though asymmetric H-bond with covalent character. The symmetric conformer with the proton in the center of the cage was found to be a transition state with a very low barrier to proton transfer along the N...N axis. Both an implicit reaction field model (IEF-PCM) and explicit placements of chloride counterions, suggested by a published X-ray crystal structure, were found to modify the position of the proton and the strength of the H-bond. An external counterion placed along the N...N axis and near one of the bridgehead nitrogens is most effective in weakening this very hydrophobically shielded diamine H-bond. The results of this study are relevant to ongoing issues about the possible participation of unusually strong H-bonds in enzymatic catalysis.