In some recent papers, a connection between optimal transport and density functional theory has been noticed. The transport model involves a cost function of Coulomb type which decreases with distance. We present some initial results on this multimarginal transport problem. In particular, we introduce a natural notion of cyclical Monge problem and we show the equality between its infimum and the  minimum in the classical Kantorovich problem. Finally, we study the problem in dimension one, building an optimal map.