The hydrogen exchange reaction H+CNH->HCN+H may be a key step in gas-phase interstellar nitrogen chemistry. It is one of the reactions supposed to cause increasing HNC depletion with increasing temperature in dense interstellar clouds. In this paper we report the results of extensive ab-initio calculations on the H+CNH<->H+HCN system that partially confirm this hypothesis. It is shown that both forward and reverse reactions possess activation barriers. However, the activation energy of the H+CNH channel (4.2+/-1.0kcal/mol.) is four times smaller than for the endothermic HCN+H path. Calculations on the rate of the forward reaction show that tunneling under the entrance channel barrier allows a small rate coefficient at the temperatures under 100K and that the rate coefficient increases steadily with increasing temperature for T>100K.