Recent advances in nanofluidics have allowed the exploration of ion transport down to molecular-scale confinement, yet artificial porins are still far from reaching the advanced functionalities of biological ion machinery. Achieving single ion transport that is tunable by an external gate-the ionic analogue of electronic Coulomb blockade-would open new avenues in this quest. However, an understanding of ionic Coulomb blockade beyond the electronic analogy is still lacking. Here, we show that the many-body dynamics of ions in a charged nanochannel result in quantized and strongly nonlinear ionic transport, in full agreement with molecular simulations. We find that ionic Coulomb blockade occurs when, upon sufficient confinement, oppositely charged ions form 'Bjerrum pairs', and the conduction proceeds through a mechanism reminiscent of Onsager's Wien effect. Our findings open the way to novel nanofluidic functionalities, such as an ion pump based on ionic Coulomb blockade, inspired by its electronic counterpart.