  In Einstein-Maxwell-Chern-Simons theory the extremal Reissner-Nordstr\"om
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-Nordstr\"om solution. On the
other hand, not all near horizon solutions are also realized as global
solutions
