A theory is constructed for dense ionic solutions near charged planar walls that is valid for strong inter-ionic correlations. This theory predicts a fluctuation-induced, first-order transition and spontaneous charge density ordering at the interface, in the presence of an otherwise disordered bulk solution. The surface ordering is driven by applied voltage and results in an anomalous differential capacitance, in agreement with recent simulation results and consistent with experimental observations of a wide array of systems. Explicit forms for the charge density profile and capacitance are given. The theory is compared with numerical results for the charge frustrated Ising model, which is also found to exhibit a voltage driven first-order transition.Recently, experimental observations and molecular simulations have suggested a link between long-range structural correlations and the electrochemical response of a double layer capacitor composed of an ionic liquid electrolyte [1][2][3]. Specifically, these observations have alluded to a possible singular response of the differential capacitance to changes in the applied electric potential [4]. It has been postulated on the basis of molecular simulations that this response results from a competition between entropic effects of packing and local constraints of electric neutrality within the ionic liquid near a planar, constant potential electrode [5]. Using general arguments, I construct an effective field theory for a symmetric solution of dense ionic media that validates this proposal. This theory explains the observed anomalous capacitance as a result of a first-order interfacial transition associated with spontaneous charge ordering at the electrode surface.The interface between a dense ionic solution and a metal electrode has been the subject of much recent study, due to the development of ionic liquid-based supercapacitors that exploit charge separation to create high power energy storage devices [6,7]. Such concentrated electrolyte solutions exhibit inter-ionic correlations that render typical mean-field theories developed for dilute solutions, such as Gouy-Chapman-Stern theory [8], not applicable. Extensions of these theories to account for excluded volume have been developed [9][10][11][12], which are capable of capturing interfacial layering and a nonmonotonic capacitance as a function of applied potential. However, such extensions typically assume a linearly responding charge density, which necessitates that their predicted response functions are bounded. This contrasts molecular dynamics simulations of a model of BMIM + PF − 6 on graphite electrodes that indicates a voltage driven structural transition and divergent capacitance [5]. Experimental indications of similar emergent long-ranged correlations have been observed in many systems, including spontaneous two-dimensional ordering of PF 6 on gold [13] and free surfaces [14], as well as observations of hysteresis upon voltage cycling of C 9 MIM + Tf 2 N − on epitaxial graphene [3] with observed structur...