We theoretically investigate light propagation and electromagnetically induced transparency (EIT) in a quasi one-dimensional gas in which atoms interact strongly via exchange interactions. We focus on the case in which the gas is initially prepared in a many-body state that contains a single excitation and conduct a detailed study of the absorptive and dispersive properties of such a medium. This scenario is achieved in interacting gases of Rydberg atoms with two relevant $S$-states that are coupled through exchange. Of particular interest is the case in which the medium is prepared in an entangled spinwave state. This, in conjunction with the exchange interaction, gives rise to a non-local susceptibilty which --- in comparison to conventional Rydberg EIT --- qualitatively alters the absorption and propagation of weak probe light, leading to non-local propagation and enhanced absorption. ; Comment: 5 pages, 4 figures