In the Einstein-Maxwell-Chern-Simons theory the extremal Reissner-Nordström solution is no longer the single extremal solution with vanishing angular momentum, when the Chern-Simons coupling constant reaches a critical value. Instead a whole sequence of rotating extremal J=0 solutions arises, labeled by the node number of the magnetic U(1) potential. Associated with the same near horizon solution, the mass of these radially excited extremal solutions converges to the mass of the extremal Reissner-Nordström solution. On the other hand, not all near horizon solutions are also realized as global solutions.